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HTML

              
                <div id="top"><h1>XCalc.js Derivative Demo</h1>
  	<div id="function">
      <label>y = </label><input type="text" value="d/dx (x+4)^2*(x-6)+60sinx" id="input" />
  	</div>
  	<div id="range">
  		<div class="rangeSection">From <input type="text" value="" placeholder="-10" id="x1" /> &lt; x &lt; <input type="text" value="" placeholder="10" id="x2" /></div>
      <div class="rangeSection">and <input type="text" placeholder="auto" value="" id="y1" /> &lt; y &lt; <input type="text" placeholder="auto" value="" id="y2" /></div>
  	</div>
  	<input type="button" value="Graph" id="graph" />
  </div>
  <div id="wrapper">
    <div id="result"></div>
  </div>
  <a id="github" href="https://github.com/pahgawk/XCalc">Find this on Github!</a>
              
            
!

CSS

              
                @import url(https://fonts.googleapis.com/css?family=Open+Sans:300);

body {
  background-color:#34495e;
  color:#FFF;
  font-family: sans-serif;
  padding:0;
  margin:0;
  text-align:center;
}
#github {
  position:absolute;
  top:0;
  right:0;
  padding:20px;
  background-color:#123;
  color:#FFF;
  text-decoration:none;
}
#github:hover {
  background-color:#234;
}
#top {
  padding:20px;
  display:inline-block;
}
h1 {
  font-family: 'Open Sans', sans-serif;
  font-size:30px;
  margin:0 0 10px 0;
}
input[type="submit"], input[type="button"], a.button {
	background-color:#FFF;
	color:#000;
	padding:5px;
	border: 5px solid #FFF;
	text-decoration:none;
	display:inline-block;
  height:40px;
  font-size:16px;
  font-family:sans-serif;
  margin:0 0 0 10px;
}
input[type="submit"]:hover, input[type="button"]:hover, a.button:hover {
	border: 5px solid #DDD;
}
input[type="text"] {
  display:inline-block;
  font-size: inherit;
  padding: 10px;
  border: 0;
}
input[type="text"]:focus {
  outline: 0;
  background-color:#EEE;
}
#function {
  margin-bottom:20px;
}
#function label {
  display:inline-block;
  height:40px;
  line-height:40px;
  margin-right:5px;
}
#function input[type="text"] {
  margin:0;
  width:85%;
  display:inline-block;
  height:20px;
  float:right;
}
#range {
  color: #9AB;
}
#range input[type="text"] {
  width:30px;
  height:15px;
  text-align:center;
  color: #9AB;
  background-color:#2c3e50;
}
#range input[type="text"]::-webkit-input-placeholder{
  color: #9AB;
}
#range input[type="text"]:-moz-placeholder{
  color: #9AB;
}
#range input[type="text"]::-moz-placeholder {
  color: #9AB;
}
#range input[type="text"]:-ms-input-placeholder {
  color: #9AB;
}
#range input[type="text"]:focus {
  background-color:#2e4052;
}
.rangeSection {
  display:inline-block;
}
#graph {
  margin:20px auto 0 auto;
  width: 100%;
  height:50px;
}
#result {
  margin-top:10px;
  border-top:20px solid #2c3e50;
  border-bottom:20px solid #2c3e50;
  overflow:hidden;
  background-color:#2c3e50;
  text-align:center;
  max-height:0;
  margin-bottom:20px;
  -webkit-transition: all 0.3s ease-out;
  -moz-transition: all 0.3s ease-out;
  -ms-transition: all 0.3s ease-out;
  -o-transition: all 0.3s ease-out;
  transition: all 0.3s ease-out;
}
.open #result {
  max-height:2000px;
  padding:20px;
  color:#FFF;
}
canvas {
  margin-bottom: 50px;
}
canvas:last-child {
  margin-bottom: 10px;
}
.answer {
  clear:both;
  text-align:center;
}
.final {
  color:#FFF;
  font-size:60px;
  text-align:left;
  font-family: 'Open Sans', sans-serif;
}
.error {
  background-color:#6B1010;
  padding:10px;
  opacity:0.7;
  display:inline-block;
  width:500px;
  text-align:left;
}

/* Pretty formula styles */
.formula {
  font-family: 'Open Sans', sans-serif;
  padding:0 10px;
  margin-bottom:10px;
}
.group {
  display:inline-block;
  vertical-align:baseline;
  text-align:center;
  margin:1px 1px 0 0;
  padding:0;
}
.division {
  vertical-align: middle;
}
.operator {
  padding:5px;
}
.exponent {
  font-size: 0.7em;
  vertical-align:super;
}
.denom {
  clear:both;
  display:block;
  border-top:1px solid #FFF;
  padding:0 20px;
}

@media all and (max-width:700px) {
  #github {
    position:relative;
    width:auto;
    display:block;
  }
  h1 {
    font-size:24px; 
  }
}

@media all and (max-width:500px) {
  #top {
    display:block;
    position:relative;
  }
  #function label {
    width:10%;
    text-align:right;
  }
  #function input[type="text"] {
    width:70%;
  }
  .rangeSection {
    display:block;
    margin-bottom:5px;
  }
}
              
            
!

JS

              
                //Class for operators
function Operator(input) {
  this.operator = input;
  if (!input) {
    XCalc.log("Operator has no input.");
  }

  this.solve = function(segment1, segment2, x) {
    var v1 = segment1.coefficient;
    if (segment1.type=="variable") {
      v1 = x;
    }
    var v2 = segment2.coefficient;
    if (segment2.type=="variable") {
      v2 = x;
    }
    if (this.operator=="+") {
      return new Segment(v1 + v2);
    } else if (this.operator=="-") {
      return  new Segment(v1 - v2);
    } else if  (this.operator=="*") {
      return  new Segment(v1 * v2);
    } else if (this.operator=="/") {
      return  new Segment(v1 / v2);
    } else if (this.operator=="^") {
      return  new Segment(Math.pow(v1, v2));
    }
  };
}

//Class for special functions
function MathFunction(input) {
  this.f=input;
  if (!input) {
    XCalc.log("Math function has no input.");
  }

  this.solve = function(segment) {
    var v = segment.coefficient;
    if (this.f=="sin") {
      return new Segment(Math.sin(v));
    } else if (this.f=="cos") {
      return new Segment(Math.cos(v));
    } else if (this.f=="tan") {
      return new Segment(Math.tan(v));
    } else if (this.f=="asin") {
      return new Segment(Math.asin(v));
    } else if (this.f=="acos") {
      return new Segment(Math.acos(v));
    } else if (this.f=="atan") {
      return new Segment(Math.atan(v));
    } else if (this.f=="abs") {
      return new Segment(Math.abs(v));
    } else if (this.f=="log") {
      return new Segment(Math.log(v)/Math.log(10));
    } else if (this.f=="ln") {
      return new Segment(Math.log(v));
    }
  };
}

//Class for a segment of math (a container)
function Segment(input) {
  this.sections = [];
  this.type="section";
  this.operator=0;
  this.coefficient=0;
  this.mathFunction=0;
  this.variable="";

  var removeBrackets = function(value) {
    if (!value) return "";

    //While there are brackets around the string
    while (value.substr(0, 1)=="(" && value.substr(value.length-1, 1)==")") {
      var openBrackets=1;

      //See if the end bracket closes the opening bracket or not
      for (var i=1; i<value.length&&openBrackets>0; i++) {
        if (value.substr(i, 1)=="(") openBrackets++;
        if (value.substr(i, 1)==")") openBrackets--;
      }
      i-=1;

      //If it corresponds to different brackets, do nothing
      if (openBrackets!==0 || i!=value.length-1) {
        break;

      //Otherwise, remove the brackets, continue loop to see if there are more
      } else {
        value=value.substring(1, value.length-1);
      }
    }

    return value;
  };

  var findLast = function(operator, value) {

    //Keep searching for the next last sign if the one found is within brackets
    var inBrackets=true;
    var index=-1;
    if (operator!="^") {
      index=value.lastIndexOf(operator);
    } else {
      index=value.indexOf(operator); //Look for the first instead of last if it's an exponent
    }
    var operators="+-/*^";
    while (inBrackets) {
      var openBrackets=0;

      //Find how many brackets are opened or closed at a given point in the string
      for (var i=0; i<value.length; i++) {
        if (value.substr(i, 1)=="(") {
          openBrackets++;
        } else if (value.substr(i, 1)==")") {
          openBrackets--;
        }

        if (i==index) {

          //If no brackets are open (and if the operator is actually - and not just a minus sign), break the loop.
          if ((openBrackets===0 && (operator!="-" || (i>0 && operators.indexOf(value.substr(i-1, 1))==-1) || i===0)) || (openBrackets==1 && operator=="(")) {
            inBrackets=false;
            break;

          //Otherwise, find the next operator, and loop through again to see if that one is in brackets
          } else {
            if (operator!="^") {
              index = value.substring(0, index).lastIndexOf(operator);
            } else {
              var nextOperator = value.substring(index+1).indexOf(operator);
              if (nextOperator==-1) {
                index=-1;
              } else {
                index = (index+1+value.substring(index+1).indexOf(operator));
              }
            }
          }
        }
      }

      //If no more operators are found, break the loop
      if (index==-1) {
        inBrackets=false;
      }
    }
    return index;
  };

  var findLastTrig = function(trig, value) {
    var matches=0;
    var index=-1;
    var r=0;
    if (trig=="sin") {
      r=/(a)?sin/g;
    } else if (trig=="cos") {
      r=/(a)?cos/g;
    } else if (trig=="tan") {
      r=/(a)?tan/g;
    } else {
      return -1;
    }
    for (matches=r.exec(value); matches; matches=r.exec(value)) if (RegExp.$1 != "a") index=matches.index;
    var inBrackets=true;
    while (inBrackets && index!=-1) {
      var openBrackets=0;

      //Find how many brackets are opened or closed at a given point in the string
      for (var i=0; i<value.length; i++) {
        if (value.substr(i, 1)=="(") {
          openBrackets++;
        } else if (value.substr(i, 1)==")") {
          openBrackets--;
        }

        if (i==index) {

          //If no brackets are open (and if the operator is actually - and not just a minus sign), break the loop.
          if (openBrackets===0) {
            inBrackets=false;
            break;

          //Otherwise, find the next operator, and loop through again to see if that one is in brackets
          } else {
            var sub = value.substring(0, index);
            index=-1;
            for (matches=r.exec(sub); matches; matches=r.exec(sub)) if (RegExp.$1 != "a") index=matches.index;
          }
        }
      }

      //If no more operators are found, break the loop
      if (index==-1) {
        inBrackets=false;
      }
    }
    return index;
  };

  //Specifically for finding brackets that can be used for multiplication
  var findMultiplicationBrackets = function(value) {

    //Keep searching for the next last sign if the one found is within brackets
    var inBracketsOpen=true;
    var inBracketsClosed=true;
    var indexOpen=-1;
    var indexClosed=-1;
    var operators="+-/*^sincostanabsloglnsqrt";
    
    indexOpen=value.lastIndexOf("(");
    indexClosed=value.lastIndexOf(")");

    while (inBracketsOpen || inBracketsClosed) {
      var openBrackets=0;

      //Find how many brackets are opened or closed at a given point in the string
      for (var i=0; i<value.length; i++) {
        if (value.substr(i, 1)=="(") {
          openBrackets++;
        } else if (value.substr(i, 1)==")") {
          openBrackets--;
        }

        if (i==indexOpen && inBracketsOpen) {

          if (openBrackets==1 && i!==0 && operators.indexOf(value.substr(i-1, 1))==-1) {
            inBracketsOpen=false;

          //Otherwise, find the next operator, and loop through again to see if that one is in brackets
          } else {
            indexOpen = value.substring(0, indexOpen).lastIndexOf("(");
          }
        }

        if (i==indexClosed && inBracketsClosed) {

          if (openBrackets===0 && i<value.length-1 && operators.indexOf(value.substr(i+1, 1))==-1) {
            inBracketsClosed=false;

          //Otherwise, find the next operator, and loop through again to see if that one is in brackets
          } else {
            indexClosed = value.substring(0, indexClosed).lastIndexOf(")");
          }
        }
      }

      //If no more operators are found, break the loop
      if (indexOpen==-1) {
        inBracketsOpen=false;
      }
      if (indexClosed==-1) {
        inBracketsClosed=false;
      }
    }

    if (indexClosed>indexOpen && indexClosed!=-1) {
      return indexClosed;
    } else {
      return indexOpen;
    }
  };

  this.containsX = function() {
    if (this.type=="variable") {
      return true;
    } else if (this.type=="value") {
      return false;
    } else {
      if (this.sections.length==1) {
        return this.sections[0].containsX();
      } else if (this.sections.length==2) {
        return this.sections[0].containsX() || this.sections[1].containsX();
      }
    }
  };

  this.equals = function(expression) {
    if (this.type != expression.type) {
      return false;
    } else {
      if (this.type=="function") {
        return (this.mathFunction.f==expression.mathFunction.f && this.sections[0].equals(expression.sections[0]));
      } else if (this.type=="variable") {
        return (this.variable==expression.variable && this.coefficient==expression.coefficient);
      } else if (this.type=="value") {
        return this.coefficient==expression.coefficient;
      } else if (this.type=="section") {
        if (this.operator.operator=="*" || this.operator.operator=="+") {
          return (this.operator.operator==expression.operator.operator && ((this.sections[0].equals(expression.sections[0]) && this.sections[1].equals(expression.sections[1])) || (this.sections[0].equals(expression.sections[1]) && this.sections[1].equals(expression.sections[0]))));
        } else {
          return (this.operator.operator==expression.operator.operator && this.sections[0].equals(expression.sections[0]) && this.sections[1].equals(expression.sections[1]));
        }
      }
    }
  };

  //Recursively solve children
  this.solve = function(x) {
    if (!x) x=0;
    if (this.type=="value") {
      return this;
    } else if (this.type=="variable") {
      return new Segment(x);
    } else if (this.type=="function") {
      return this.mathFunction.solve(this.sections[0].solve(x));
    } else {
      if (this.sections.length==1) {
        return this.sections[0].solve(x);
      } else if (this.sections.length==2) {
        return this.operator.solve(this.sections[0].solve(x), this.sections[1].solve(x), x);
      }
    }
  };

  //Outputs the final answer
  this.result = function(x) {
    return this.solve(x).coefficient;
  };

  this.simplify = function() {
    var expression = new Segment(this);
    var final;

    //If the segment is a variable, leave it as is.
    //If it contains a variable in its subsections, simplify subsections
    if (expression.containsX() && expression.type!="variable") {
      for (var i=0; i<expression.sections.length; i++) {
        expression.sections[i] = expression.sections[i].simplify();
      }
      if (expression.type=="section") {
        if (expression.operator.operator == "+") {
          if (expression.sections[0].type=="value" && expression.sections[0].coefficient===0) {
            expression=expression.sections[1];
          } else if (expression.sections[1].type=="value" && expression.sections[1].coefficient===0) {
            expression=expression.sections[0];
          }
        } else if (expression.operator.operator == "-") {
          if (expression.sections[1].type=="value" && expression.sections[1].coefficient===0) {
            expression=expression.sections[1];
          }
        } else if (expression.operator.operator == "*") {
          if (expression.sections[0].type=="value" && expression.sections[0].coefficient==1) {
            expression = new Segment(expression.sections[1]);
          } else if (expression.sections[1].type=="value" && expression.sections[1].coefficient==1) {
            expression = new Segment(expression.sections[0]);
          } else if ((expression.sections[0].type=="value" && expression.sections[0].coefficient===0) || (expression.sections[1].type=="value" && expression.sections[1].coefficient===0)) {
            expression = new Segment(0);
          } else if (expression.sections[1].type=="section" && expression.sections[1].operator.operator=="/" && expression.sections[1].sections[0].type=="value" && expression.sections[1].sections[0].coefficient==1) {
            expression.operator = new Operator("/");
            expression.sections[1]=expression.sections[1].sections[1];
          } else if (expression.sections[0].type=="section" && expression.sections[0].operator.operator=="/" && expression.sections[0].sections[0].type=="value" && expression.sections[0].sections[0].coefficient==1) {
            expression.operator = new Operator("/");
            var num = expression.sections[1];
            expression.sections[1] = expression.sections[0].sections[1];
            expression.sections[0] = num;
          } else if (expression.sections[0].type=="section" && expression.sections[0].operator.operator=="^" && expression.sections[1].type=="section" && expression.sections[1].operator.operator=="^" && expression.sections[0].sections[0].equals(expression.sections[1].sections[0])) {
            var exponent = new Segment(0);
            exponent.type="section";
            exponent.sections.push(expression.sections[0].sections[1]);
            exponent.sections.push(expression.sections[1].sections[1]);
            exponent.operator = new Operator("+");
            expression.sections[0]=expression.sections[0].sections[0];
            expression.sections[1]=exponent;
            expression.operator = new Operator("^");
          } else if (expression.sections[0].type=="section" && expression.sections[0].operator.operator=="*") {
            final = new Segment(0);
            final.operator = new Operator("*");
            final.type="section";
            if (!expression.sections[0].sections[1].containsX()) {
              if (expression.sections[0].sections[0].containsX()) {
                final.sections.push(expression.sections[0].sections[0]);
                final.sections.push(expression.sections[1]);
                expression.sections[0]=expression.sections[0].sections[1];
                expression.sections[1]=final;
              } else {
                final.sections.push(expression.sections[0].sections[1]);
                final.sections.push(expression.sections[1]);
                expression.sections[0]=expression.sections[0].sections[0];
                expression.sections[1]=final;
              }
            } else if (!expression.sections[0].sections[0].containsX()) {
              if (expression.sections[0].sections[1].containsX()) {
                final.sections.push(expression.sections[0].sections[1]);
                final.sections.push(expression.sections[1]);
                expression.sections[0]=expression.sections[0].sections[0];
                expression.sections[1]=final;
              } else {
                final.sections.push(expression.sections[0].sections[0]);
                final.sections.push(expression.sections[1]);
                expression.sections[0]=expression.sections[0].sections[1];
                expression.sections[1]=final;
              }
            }
          } else if (expression.sections[1].type=="section" && expression.sections[1].operator.operator=="*") {
            final = new Segment(0);
            final.operator = new Operator("*");
            final.type="section";
            if (!expression.sections[1].sections[1].containsX()) {
              if (expression.sections[1].sections[0].containsX()) {
                final.sections.push(expression.sections[1].sections[0]);
                final.sections.push(expression.sections[0]);
                expression.sections[1]=expression.sections[1].sections[1];
                expression.sections[0] = final;
              } else {
                final.sections.push(expression.sections[1].sections[1]);
                final.sections.push(expression.sections[0]);
                expression.sections[1]=expression.sections[1].sections[0];
                expression.sections[0] = final;
              }
            } else if (!expression.sections[1].sections[0].containsX()) {
              if (expression.sections[1].sections[1].containsX()) {
                final.sections.push(expression.sections[1].sections[1]);
                final.sections.push(expression.sections[0]);
                expression.sections[1]=(expression.sections[1].sections[0]);
                expression.sections[0] = final;
              } else {
                final.sections.push(expression.sections[1].sections[0]);
                final.sections.push(expression.sections[0]);
                expression.sections[1]=(expression.sections[1].sections[1]);
                expression.sections[0] = final;
              }
            }
          }
        } else if (expression.operator.operator == "/") {
          if (expression.sections[1].type=="value" && expression.sections[1].coefficient==1) {
            expression = expression.sections[0];
          } else if (expression.sections[0].equals(expression.sections[1])) {
            expression = new Segment(1);
          } else if (expression.sections[0].type=="section" && expression.sections[0].operator.operator=="^" && expression.sections[1].type=="section" && expression.sections[1].operator.operator=="^" && expression.sections[0].sections[0].equals(expression.sections[1].sections[0])) {
            var exponent2 = new Segment(0);
            exponent2.type="section";
            exponent2.sections.push(expression.sections[0].sections[1]);
            exponent2.sections.push(expression.sections[1].sections[1]);
            exponent2.operator = new Operator("-");
            expression.sections[0]=expression.sections[0].sections[0];
            expression.sections[1]=exponent2;
            expression.operator = new Operator("^");
          }
        } else if (expression.operator.operator == "^") {
          if (expression.sections[1].type=="value" && expression.sections[1].coefficient==1) {
            expression = expression.sections[0];
          } else if (expression.sections[1].type=="value" && expression.sections[1].coefficient===0) {
            expression = new Segment(0);
          } else if (expression.sections[0].type=="value" && expression.sections[0].coefficient==1) {
            expression = new Segment(1);
          } else if (expression.sections[0].type=="section" && (expression.sections[0].operator.operator=="/" || expression.sections[0].operator.operator=="/")) {
            var num2 = new Segment(0);
            num2.type="section";
            num2.operator = new Operator("^");
            num2.sections.push(expression.sections[0].sections[0]);
            num2.sections.push(expression.sections[1]);

            var denom = new Segment(0);
            denom.type="section";
            denom.operator = new Operator("^");
            denom.sections.push(expression.sections[0].sections[1]);
            denom.sections.push(expression.sections[1]);

            expression.operator = expression.sections[0].operator;
            expression.sections[0] = num2;
            expression.sections[1] = denom;
          }
        }
      }

    //If it can be simplified to a value, simplify
    } else if (expression.type!="variable") {
      expression.coefficient = expression.result();
      expression.type="value";
    }

    //Keep simplifying until it's the same
    if (this.equals(expression)) {
      return this;
    } else {
      return expression.simplify();
    }
  };

  this.derivative = function() {
    var expression = new Segment(this);
    var deriv = new Segment(0);
    var s1, s2, s3, s4;

    if (expression.type=="variable") {
      deriv.coefficient = 1;
    } else if (expression.type == "value" || !expression.containsX()) {
      deriv.coefficient = 0;
    } else if (expression.type=="section" && expression.operator.operator!="^") {

      //+/- rules
      if (expression.operator.operator == "+") {
        deriv.type = "section";
        deriv.sections.push(expression.sections[0].derivative());
        deriv.sections.push(expression.sections[1].derivative());
        deriv.operator = new Operator("+");
      } else if (expression.operator.operator == "-") {
        deriv.type = "section";
        deriv.sections.push(expression.sections[0].derivative());
        deriv.sections.push(expression.sections[1].derivative());
        deriv.operator = new Operator("-");

      //Product rule
      } else if (expression.operator.operator == "*") {
        s1 = new Segment(0);
        s1.type = "section";
        s1.sections.push(expression.sections[0].derivative());
        s1.sections.push(expression.sections[1]);
        s1.operator = new Operator("*");

        s2 = new Segment(0);
        s2.type = "section";
        s2.sections.push(expression.sections[0]);
        s2.sections.push(expression.sections[1].derivative());
        s2.operator = new Operator("*");

        deriv.type = "section";
        deriv.sections.push(s1);
        deriv.sections.push(s2);
        deriv.operator = new Operator("+");

      //Quotient rule
      } else if (expression.operator.operator == "/") {
        s1 = new Segment(0);
        s1.type = "section";
        s1.sections.push(expression.sections[0].derivative());
        s1.sections.push(expression.sections[1]);
        s1.operator = new Operator("*");

        s2 = new Segment(0);
        s2.type = "section";
        s2.sections.push(expression.sections[1].derivative());
        s2.sections.push(expression.sections[0]);
        s2.operator = new Operator("*");

        var num = new Segment(0);
        num.type = "section";
        num.sections.push(s1);
        num.sections.push(s2);
        num.operator = new Operator("-");

        var denom = new Segment(0);
        denom.type = "section";
        denom.sections.push(expression.sections[1]);
        denom.sections.push(new Segment(2));
        denom.operator = new Operator("^");

        deriv.type = "section";
        deriv.sections.push(num);
        deriv.sections.push(denom);
        deriv.operator = new Operator("/");
      }

    //functions
    } else {
      var uprime;

      s1 = new Segment(0);

      s1.type = "section";

      //Exponents
      if (expression.type == "section" && expression.operator.operator=="^") {

        //Implicitly derive ln(y)
        if (expression.sections[1].containsX() && expression.sections[0].containsX()) {
          s1 = expression;

          s2 = new Segment(0);
          s2.type = "function";
          s2.sections.push(expression.sections[0]);
          s2.mathFunction = new MathFunction("ln");

          s3 = new Segment(0);
          s3.type="section";
          s3.sections.push(expression.sections[1]);
          s3.sections.push(s2);
          s3.operator = new Operator("*");

          uprime = s3.derivative();

        //Power rule
        } else if (expression.sections[1].containsX()) {
          s2 = new Segment(0);
          s2.type = "function";
          s2.sections.push(expression.sections[0]);
          s2.mathFunction = new MathFunction("ln");

          s1.sections.push(expression);
          s1.sections.push(s2);
          s1.operator = new Operator("*");

          uprime = expression.sections[1].derivative();

        //Polynomial rule
        } else {
          var exp = new Segment(0);
          exp.type = "section";
          exp.sections.push(expression.sections[1]);
          exp.sections.push(new Segment(1));
          exp.operator = new Operator("-");

          s2 = new Segment(0);
          s2.type = "section";
          s2.sections.push(expression.sections[0]);
          s2.sections.push(exp);
          s2.operator = new Operator("^");

          s1.sections.push(expression.sections[1]);
          s1.sections.push(s2);
          s1.operator = new Operator("*");

          uprime = expression.sections[0].derivative();
        }
      } else {
        uprime = expression.sections[0].derivative();

        if (expression.mathFunction.f=="ln") {
          s1.sections.push(new Segment(1));
          s1.sections.push(expression.sections[0]);
          s1.operator = new Operator("/");

        } else if (expression.mathFunction.f=="log") {
          s2 = new Segment(0);
          s2.mathFunction = new MathFunction("ln");
          s2.type="function";
          s2.sections.push(new Segment(10));

          s3 = new Segment(0);
          s3.type="section";
          s3.sections.push(expression.sections[0]);
          s3.sections.push(s2);
          s3.operator = new Operator("*");

          s1.sections.push(new Segment(1));
          s1.sections.push(s3);
          s1.operator = new Operator("/");

        } else if (expression.mathFunction.f=="sin") {
          s1.mathFunction = new MathFunction("cos");
          s1.type="function";
          s1.sections.push(expression.sections[0]);

        } else if (expression.mathFunction.f=="cos") {
          s2 = new Segment(0);
          s2.mathFunction = new MathFunction("sin");
          s2.type="function";
          s2.sections.push(expression.sections[0]);

          s1.sections.push(new Segment(0));
          s1.sections.push(s2);
          s1.operator = new Operator("-");

        } else if (expression.mathFunction.f=="tan") {
          s2 = new Segment(0);
          s2.mathFunction = new MathFunction("cos");
          s2.type="function";
          s2.sections.push(expression.sections[0]);

          s3 = new Segment(0);
          s3.type="section";
          s3.sections.push(s2);
          s3.sections.push(new Segment(2));
          s3.operator = new Operator("^");

          s1.sections.push(new Segment(1));
          s1.sections.push(s3);
          s1.operator = new Operator("/");

        } else if (expression.mathFunction.f=="asin") {
          s2 = new Segment(0);
          s2.type="section";
          s2.sections.push(expression.sections[0]);
          s2.sections.push(new Segment(2));
          s2.operator=new Operator("^");

          s3 = new Segment(0);
          s3.type="section";
          s3.sections.push(new Segment(1));
          s3.sections.push(s2);
          s3.operator = new Operator("-");

          s4 = new Segment(0);
          s4.type="section";
          s4.sections.push(s3);
          s4.sections.push(new Segment(0.5));
          s4.operator = new Operator("^");

          s1.sections.push(new Segment(1));
          s1.sections.push(s4);
          s1.operator = new Operator("/");
        
        } else if (expression.mathFunction.f=="acos") {
          s2 = new Segment(0);
          s2.type="section";
          s2.sections.push(expression.sections[0]);
          s2.sections.push(new Segment(2));
          s2.operator=new Operator("^");

          s3 = new Segment(0);
          s3.type="section";
          s3.sections.push(new Segment(1));
          s3.sections.push(s2);
          s3.operator = new Operator("-");

          s4 = new Segment(0);
          s4.type="section";
          s4.sections.push(new Segment(0));
          s4.sections.push(new Segment(1));
          s4.operator = new Operator("-");

          var s5 = new Segment(0);
          s5.type="section";
          s5.sections.push(s3);
          s5.sections.push(new Segment(0.5));
          s5.operator = new Operator("^");

          s1.sections.push(s4);
          s1.sections.push(s5);
          s1.operator = new Operator("/");
        
        } else if (expression.mathFunction.f=="atan") {
          s2 = new Segment(0);
          s2.type="section";
          s2.sections.push(expression.sections[0]);
          s2.sections.push(new Segment(2));
          s2.operator=new Operator("^");

          s3 = new Segment(0);
          s3.type="section";
          s3.sections.push(s2);
          s3.sections.push(new Segment(1));
          s3.operator = new Operator("+");

          s1.sections.push(new Segment(1));
          s1.sections.push(s3);
          s1.operator = new Operator("/");
        
        }

      }

      //Chain rule
      deriv.type = "section";
      deriv.sections.push(s1);
      deriv.sections.push(uprime);
      deriv.operator = new Operator("*");
    }

    return deriv;
  };

  //Returns a string with the formula of the function
  this.formula = function() {
    var str = "";

    if (this.type=="value") {
      str += this.coefficient;
    } else if (this.type=="variable") {
      str += "x";
    } else if (this.type=="function") {
      str += this.mathFunction.f + "(" + this.sections[0].formula() + ")";
    } else if (this.type=="section") {
      if (this.sections[0].type=="section") {
        str+= "(" + this.sections[0].formula() + ")";
      } else {
        str+= this.sections[0].formula();
      }
      str += this.operator.operator;
      if (this.sections[1].type=="section") {
        str+= "(" + this.sections[1].formula() + ")";
      } else {
        str+= this.sections[1].formula();
      }
    }

    return str;
  };

  this.derive = function() {
    return this.simplify().derivative().simplify();
  };

  //Returns formula in divs for CSS
  this.prettyFormula = function() {
    var str="<div class='group " + this.type + ((this.type=="section" && this.operator.operator=="/")?" division":"") + "'>";

    if (this.type=="value") {
      str += this.coefficient;
    } else if (this.type=="variable") {
      str += "x";
    } else if (this.type=="function") {
      str += this.mathFunction.f + "(" + this.sections[0].prettyFormula() + ")";
    } else if (this.type=="section") {
      if (this.sections[0].type=="section" && this.sections[0].operator.operator!="/") {
        str+= "(" + this.sections[0].prettyFormula() + ")";
      } else {
        str+= this.sections[0].prettyFormula();
      }
      if (this.operator.operator=="*") {
        str += "<span class='operator'>&times</span>";
      } else if (this.operator.operator!="^" && this.operator.operator!="/") {
        str += "<span class='operator'>" + this.operator.operator + "</span>";
      }
      if (this.operator.operator=="^") {
        str += "<div class='group exponent'>" + this.sections[1].prettyFormula() + "</div>";
      } else if (this.operator.operator == "/") {
        str += "<div class='group denom'>" + this.sections[1].prettyFormula() + "</div>";
      } else {
        if (this.sections[1].type=="section" && this.sections[0].operator.operator!="/") {
          str+= "(" + this.sections[1].prettyFormula() + ")";
        } else {
          str+= this.sections[1].prettyFormula();
        }
      }
    }
    str+="</div>";
    return str;
  };

  //constructor: parse the string
  if (input!==undefined) {
    if (typeof(input)=="string") {
      //Remove excess whitespace
      input = input.replace(/\s/g, "");

      //get rid of unnecessary brackets surrounding the section
      input = removeBrackets(input);
      
      //Find the last instance of each operator in the string
      var addition = findLast("+", input);
      var subtraction = findLast("-", input);
      var division = findLast("/", input);
      var exponent = findLast("^", input); //Find the first exponent, since those work in reverse
      var bracket1 = findLast("(", input);

      var sin = findLastTrig("sin", input);
      var cos = findLastTrig("cos", input);
      var tan = findLastTrig("tan", input);
      var asin = findLast("asin", input);
      var acos = findLast("acos", input);
      var atan = findLast("atan", input);
      var abs = findLast("abs", input);
      var log = findLast("log", input);
      var ln = findLast("ln", input);
      var sqrt = findLast("sqrt", input);
      var multiplication = findLast("*", input);
      var multiplication2 = findMultiplicationBrackets(input); //Find brackets that are the same as multiplication
      var xMultiplication = findLast("x", input);
      var xMultiplication2 = findLast("X", input);
      if (xMultiplication2>xMultiplication) xMultiplication = xMultiplication2;
      var functionMultiplication = -1;
      var operators="+-/*^sincostanabsloglnsqrt";
      if (sin>multiplication && (sin===0 || operators.indexOf(input.substr(sin-1, 1))==-1)) functionMultiplication=sin;
      if (cos>multiplication && (cos===0 || operators.indexOf(input.substr(cos-1, 1))==-1)) functionMultiplication=cos;
      if (tan>multiplication && (tan===0 || operators.indexOf(input.substr(tan-1, 1))==-1)) functionMultiplication=tan;
      if (asin>multiplication && (asin===0 || operators.indexOf(input.substr(asin-1, 1))==-1)) functionMultiplication=asin;
      if (acos>multiplication && (acos===0 || operators.indexOf(input.substr(acos-1, 1))==-1)) functionMultiplication=acos;
      if (atan>multiplication && (atan===0 || operators.indexOf(input.substr(atan-1, 1))==-1)) functionMultiplication=atan;
      if (abs>multiplication && (abs===0 || operators.indexOf(input.substr(abs-1, 1))==-1)) functionMultiplication=abs;
      if (log>multiplication && (log===0 || operators.indexOf(input.substr(log-1, 1))==-1)) functionMultiplication=log;
      if (ln>multiplication && (ln===0 || operators.indexOf(input.substr(ln-1, 1))==-1)) functionMultiplication=ln;
      if (sqrt>multiplication && (sqrt===0 || operators.indexOf(input.substr(sqrt-1, 1))==-1)) functionMultiplication=sqrt;
      if (xMultiplication>multiplication && (xMultiplication===0 || operators.indexOf(input.substr(xMultiplication-1, 1))==-1)) functionMultiplication=xMultiplication;

      //Push back each half of the equation into a section, in reverse order of operations
      if (addition != -1 && addition>subtraction) {
        this.sections.push(new Segment(input.substring(0, addition)));
        this.sections.push(new Segment(input.substring(addition+1)));
        this.operator = new Operator("+");
      } else if (subtraction != -1) {
        if (subtraction>0) {
          this.sections.push(new Segment(input.substring(0, subtraction)));
        } else {
          this.sections.push(new Segment(0));
        }
        this.sections.push(new Segment(input.substring(subtraction+1)));
        this.operator = new Operator("-");
      } else if (functionMultiplication > 0 && Math.max(functionMultiplication, multiplication, multiplication2, division)==functionMultiplication) {
        this.sections.push(new Segment(input.substring(0, functionMultiplication)));
        this.sections.push(new Segment(input.substring(functionMultiplication)));
        this.operator = new Operator("*");
      } else if (multiplication2 != -1 && Math.max(multiplication2, multiplication, division)==multiplication2) {
        this.sections.push(new Segment(input.substring(0, multiplication2)));
        this.sections.push(new Segment(input.substring(multiplication2)));
        this.operator = new Operator("*");
      } else if (multiplication != -1 && multiplication>division) {
        this.sections.push(new Segment(input.substring(0, multiplication)));
        this.sections.push(new Segment(input.substring(multiplication+1)));
        this.operator = new Operator("*");
      } else if (division != -1) {
        this.sections.push(new Segment(input.substring(0, division)));
        this.sections.push(new Segment(input.substring(division+1)));
        this.operator = new Operator("/");
      } else if (exponent != -1) {
        this.sections.push(new Segment(input.substring(0, exponent)));
        this.sections.push(new Segment(input.substring(exponent+1)));
        this.operator = new Operator("^");
      } else if (sin != -1 && Math.max(sin, cos, tan, asin, acos, atan, abs, log, ln, sqrt)==sin) {
        this.sections.push(new Segment(input.substring(sin+3)));
        this.mathFunction = new MathFunction("sin");
        this.type = "function";
      } else if (cos != -1 && Math.max(cos, tan, asin, acos, atan, abs, log, ln, sqrt)==cos) {
        this.sections.push(new Segment(input.substring(cos+3)));
        this.mathFunction = new MathFunction("cos");
        this.type = "function";
      } else if (tan != -1 && Math.max(tan, asin, acos, atan, abs, log, ln, sqrt)==tan) {
        this.sections.push(new Segment(input.substring(tan+3)));
        this.mathFunction = new MathFunction("tan");
        this.type = "function";
      } else if (asin != -1 && Math.max(asin, acos, atan, abs, log, ln, sqrt)==asin) {
        this.sections.push(new Segment(input.substring(asin+4)));
        this.mathFunction = new MathFunction("asin");
        this.type = "function";
      } else if (acos != -1 && Math.max(acos, atan, abs, log, ln, sqrt)==acos) {
        this.sections.push(new Segment(input.substring(acos+4)));
        this.mathFunction = new MathFunction("acos");
        this.type = "function";
      } else if (atan != -1 && Math.max(atan, abs, log, ln, sqrt)==atan) {
        this.sections.push(new Segment(input.substring(atan+4)));
        this.mathFunction = new MathFunction("atan");
        this.type = "function";
      } else if (abs != -1 && Math.max(abs, log, ln, sqrt)==abs) {
        this.sections.push(new Segment(input.substring(abs+3)));
        this.mathFunction = new MathFunction("abs");
        this.type = "function";
      } else if (log != -1 && Math.max(log, ln, sqrt)==log) {
        this.sections.push(new Segment(input.substring(log+3)));
        this.mathFunction = new MathFunction("log");
        this.type = "function";
      } else if (ln != -1 && Math.max(ln, sqrt)==ln) {
        this.sections.push(new Segment(input.substring(ln+2)));
        this.mathFunction = new MathFunction("ln");
        this.type = "function";
      } else if (sqrt != -1) {
        this.sections.push(new Segment(input.substring(sqrt+4)));
        this.sections.push(new Segment("0.5"));
        this.operator = new Operator("^");
      } else if (bracket1 != -1) {
        var openBrackets=1;
        for (var i=bracket1+1; i<input.length&&openBrackets>0; i++) {
          if (input.substr(i, 1)=="(") openBrackets++;
          if (input.substr(i, 1)==")") openBrackets--;
        }
        if (openBrackets===0) {
          var bracket2=i-1;
          if (bracket1>0) this.sections.push(new Segment(input.substring(0, bracket1)));
          if (bracket2-bracket1!=1) this.sections.push(new Segment(input.substring(bracket1+1, bracket2)));
          if (bracket2!=input.length-1) this.sections.push(new Segment(input.substring(bracket2+1)));
          this.operator = new Operator("*");
        } else {
          XCalc.log("Brackets nesting error: " + input);
        }

      //If there are no operators, just push the input itself
      } else {
        var xLocation=input.toLowerCase().indexOf("x");
        if (xLocation!=-1) {
          if (xLocation>0) {
            this.sections.push(new Segment(input.substring(0, xLocation)));
            this.sections.push(new Segment("x"));
            this.operator=new Operator("*");
          } else {
            this.variable="x";
            this.type="variable";
          }
        } else {
          this.coefficient = parseFloat(input);
          this.type = "value";
        }
      }
    } else if (typeof(input)=="number") {
      this.coefficient = input;
      this.type = "value";
    } else if (input.simplify) {
      this.coefficient = input.coefficient;
      this.operator = input.operator;
      this.mathFunction = input.mathFunction;
      this.variable = input.variable;
      this.type=input.type;
      this.sections=[];
      for (var j=0; j<input.sections.length; j++) {
        this.sections.push(new Segment(input.sections[j]));
      }
    }
  } else {
    XCalc.log("Segment has no input.");
  }
}


//One point on a graph
function Point(x, y) {
  this.x = x;
  this.y = y;
}


//MathFunction to create graphs
function Graph(value, width, height, startx1, startx2, starty1, starty2) {
  var autoRange=(starty1===undefined || starty1=="auto");

  //Properties
  if (typeof(value)=="string") {
    this.expression = new Segment(value);
  } else {
    this.expression = value;
  }
  var points = [];
  var canvas = document.createElement("canvas");
  canvas.width=width || 400;
  canvas.height=height || 400;
  var graphCanvas = document.createElement("canvas");
  graphCanvas.width = canvas.width;
  graphCanvas.height = canvas.height;
  var min;
  var max;
  var x1 = (startx1===undefined)?-10:startx1;
  var x2 = (startx2===undefined)?10:startx2;
  var y1 = (starty1===undefined)?-10:starty1;
  var y2 = (starty2===undefined)?10:starty2;
  var startMouse = new Point(0, 0);
  var mousePos = new Point(0, 0);
  var stage=0;
  var graphStage=0;
  var img=0;
  var timer=0;
  var distX=0;
  var distY=0;

  //Gets minimum y value in the set of points
  this.getMin = function() {
    if (min===undefined) {
      if (points.length>0) {
        var i=0;
        while (isNaN(points[i].y) || points[i].y === undefined || Math.abs(points[i].y) == Infinity) i++;
        var _min = points[i].y;
        for (i++; i<points.length; i++) {
          if (points[i].y<_min) _min = points[i].y;
        }
        min=_min;
        return min;
      } else {
        return 0;
      }
    } else {
      return min;
    }
  };

  //Gets maximum y value in the set of points
  this.getMax = function() {
    if (max===undefined) {
      if (points.length>0) {
        var i=0;
        while (isNaN(points[i].y) || points[i].y === undefined || Math.abs(points[i].y) == Infinity) i++;
        var _max = points[i].y;
        for (i++; i<points.length; i++) {
          if (points[i].y>_max) _max = points[i].y;
        }
        max=_max;
        return max;
      } else {
        return 0;
      }
    } else {
      return max;
    }
  };

  //Updates the points and graph
  this.update = function() {
    var accuracy = (x2-x1)/canvas.width;
    points = [];
    for (var i=x1; i<=x2; i+=accuracy) {
      points.push(new Point(i, this.expression.result(i)));
      if ((points[points.length-1].y!==0 && !points[points.length-1].y) || Math.abs(points[points.length-1].y)>10000) {
        points[points.length-1].y=undefined;
      }
    }
    max=undefined;
    min=undefined;

    if (autoRange) {
      if (this.getMax()-this.getMin()>100000) {
        y1=-100;
        y2=100;
      } else {
        y1=this.getMin()-5;
        y2=this.getMax()+5;
      }
      autoRange = false;
    }

    this.redraw();
  };

  var drawAxes = function(_x1, _x2, _y1, _y2) {
    stage.strokeStyle="#bdc3c7";
    stage.fillStyle="#bdc3c7";
    var limit=0;
    var i=0;

    //Draw the y axis if it is in the view
    if (0>=_x1-30 && 0<=_x2+30) {
      stage.lineWidth=2;
      stage.beginPath();
      stage.moveTo(canvas.width/2-(((_x2+_x1)/2)/(_x2-_x1))*canvas.width, 0);
      stage.lineTo(canvas.width/2-(((_x2+_x1)/2)/(_x2-_x1))*canvas.width, canvas.height);
      stage.closePath();
      stage.stroke();
      stage.textAlign = "right";
      stage.textBaseline="middle";

      //Draw ticks and numbers on x axis
      stage.lineWidth=1;
      limit = (Math.abs(_y2)>Math.abs(_y1))?Math.abs(_y2):Math.abs(_y1);
      for (i=0; i<=limit; i+=Math.pow(10, Math.floor(Math.log(_y2-_y1) / Math.LN10))/2) {
        if (i===0) continue;
        if (i<=_y2+50) {
          stage.beginPath();
          stage.moveTo(canvas.width/2-(((_x2+_x1)/2)/(_x2-_x1))*canvas.width-5, canvas.height-((i-_y1)/(_y2-_y1))*canvas.height);
          stage.lineTo(canvas.width/2-(((_x2+_x1)/2)/(_x2-_x1))*canvas.width+5, canvas.height-((i-_y1)/(_y2-_y1))*canvas.height);
          stage.closePath();
          stage.stroke();
          stage.fillText(""+(Math.round(i*100)/100), canvas.width/2-(((_x2+_x1)/2)/(_x2-_x1))*canvas.width-8, canvas.height-((i-_y1)/(_y2-_y1))*canvas.height);
        }

        if (i>=_y1-50) {
          stage.beginPath();
          stage.moveTo(canvas.width/2-(((_x2+_x1)/2)/(_x2-_x1))*canvas.width-5, canvas.height-((-i-_y1)/(_y2-_y1))*canvas.height);
          stage.lineTo(canvas.width/2-(((_x2+_x1)/2)/(_x2-_x1))*canvas.width+5, canvas.height-((-i-_y1)/(_y2-_y1))*canvas.height);
          stage.closePath();
          stage.stroke();
          stage.fillText(""+(Math.round(-i*100)/100), canvas.width/2-(((_x2+_x1)/2)/(_x2-_x1))*canvas.width-8, canvas.height-((-i-_y1)/(_y2-_y1))*canvas.height);
        }
      }
    }

    //Draw the x axis if it is in the view
    if (0>=_y1-50 && 0<=_y2+50) {
      stage.lineWidth=2;
      stage.beginPath();
      stage.moveTo(0, canvas.height/2+(((_y2+_y1)/2)/(_y2-_y1))*canvas.height);
      stage.lineTo(canvas.width, canvas.height/2+(((_y2+_y1)/2)/(_y2-_y1))*canvas.height);
      stage.closePath();
      stage.stroke();
      stage.textAlign = "center";
      stage.textBaseline="top";

      //Draw ticks and numbers on y axis
      stage.lineWidth=1;
      limit = (Math.abs(_x2)>Math.abs(_x1))?Math.abs(_x2):Math.abs(_x1);
      for (i=0; i<=limit; i+=Math.pow(10, Math.floor(Math.log(_x2-_x1) / Math.LN10))/2) {
        if (i===0) continue;
        if (i<=_x2+50) {
          stage.beginPath();
          stage.moveTo(((i-_x1)/(_x2-_x1))*canvas.width, canvas.height/2+(((_y2+_y1)/2)/(_y2-_y1))*canvas.height-5);
          stage.lineTo(((i-_x1)/(_x2-_x1))*canvas.width, canvas.height/2+(((_y2+_y1)/2)/(_y2-_y1))*canvas.height+5);
          stage.closePath();
          stage.stroke();
          stage.fillText(""+(Math.round(i*100)/100), ((i-_x1)/(_x2-_x1))*canvas.width, canvas.height/2+(((_y2+_y1)/2)/(_y2-_y1))*canvas.height+8);
        }

        if (i>=_x1-50) {
          stage.beginPath();
          stage.moveTo(((-i-_x1)/(_x2-_x1))*canvas.width, canvas.height/2+(((_y2+_y1)/2)/(_y2-_y1))*canvas.height-5);
          stage.lineTo(((-i-_x1)/(_x2-_x1))*canvas.width, canvas.height/2+(((_y2+_y1)/2)/(_y2-_y1))*canvas.height+5);
          stage.closePath();
          stage.stroke();
          stage.fillText(""+(Math.round(-i*100)/100), ((-i-_x1)/(_x2-_x1))*canvas.width, canvas.height/2+(((_y2+_y1)/2)/(_y2-_y1))*canvas.height+8);
        }
      }
    }
  }.bind(this);

  //Updates the canvas
  this.redraw = function() {
    if (points.length>1) {
      stage.fillStyle = "#FFFFFF";
      stage.fillRect(0, 0, canvas.width, canvas.height);
      graphStage.clearRect(0, 0, canvas.width, canvas.height);
      graphStage.lineCap="round";

      var offsetY = -y1;

      drawAxes(x1, x2, y1, y2);

      //Draw all the points
      graphStage.strokeStyle="#2980b9";
      graphStage.lineWidth=1;
      graphStage.beginPath();

      //Find the first point that exists
      var i=0;
      while (isNaN(points[i].y) || points[i].y === undefined || Math.abs(points[i].y) == Infinity) i++;
      graphStage.moveTo((i/points.length)*canvas.width, canvas.height-((points[i].y+offsetY)/(y2-y1))*canvas.height);
      for (i++; i<points.length; i++) {
        if (Math.abs((canvas.height-((points[i].y+offsetY)/(y2-y1))*canvas.height)-(canvas.height-((points[i-1].y+offsetY)/(y2-y1))*canvas.height))<=canvas.height && points[i].y !== undefined && Math.abs(points[i].y) != Infinity && !isNaN(points[i].y)) {
          graphStage.lineTo((i/(points.length-1))*canvas.width, canvas.height-((points[i].y+offsetY)/(y2-y1))*canvas.height);
        }
        if (points[i].y !== undefined && Math.abs(points[i].y) != Infinity && !isNaN(points[i].y)) {
          graphStage.moveTo((i/(points.length-1))*canvas.width, canvas.height-((points[i].y+offsetY)/(y2-y1))*canvas.height);
        } else {
          graphStage.moveTo((i/(points.length-1))*canvas.width, canvas.height-((0+offsetY)/(y2-y1))*canvas.height);
        }
      }
      graphStage.closePath();
      graphStage.stroke();

      img = graphStage.getImageData(0, 0, canvas.width, canvas.height);
      stage.drawImage(graphCanvas, 0, 0);
    } else {
      XCalc.log("Not enough points to graph.");
    }
  };

  //Updates the view of the graph
  this.setRange = function(_x1, _x2, _y1, _y2) {
    x1=_x1;
    x2=_x2;
    y1=_y1;
    y2=_y2;
    if (_y1=="auto" || _y1===undefined) autoRange=true;
    this.update();
  };

  //Gets x and y of the mouse relative to the top left of the canvas
  var getMousePos = function(evt) {
      var rect = canvas.getBoundingClientRect();
      var root = document.documentElement;
      
      // return relative mouse position
      var mouseX = evt.clientX - rect.left - root.scrollLeft;
      var mouseY = evt.clientY - rect.top - root.scrollTop;
      
      return new Point(mouseX, mouseY);
  }.bind(this);

  //Starts panning
  var startDrag = function(event) {
    document.addEventListener("mousemove", dragMouse, false);
    document.addEventListener("mouseup", endDrag, false);
    document.documentElement.style["-moz-user-select"] = "none";
    document.documentElement.style["-webkit-user-select"] = "none";
    document.documentElement.style["-khtml-user-select"] = "none";
    document.documentElement.style["user-select"] = "none";
    canvas.removeEventListener("mouseover", startMouseOver, false);
    canvas.removeEventListener("mousemove", moveMouse, false);
    startMouse = getMousePos(event);
  }.bind(this);

  //Recalculate and redraws the view based on the mouse position
  var redrawLine = function() {
    var offsetX = ((mousePos.x-startMouse.x)/canvas.width)*(x2-x1);
    var offsetY = ((mousePos.y-startMouse.y)/canvas.height)*(y2-y1);
    this.setRange(x1-offsetX, x2-offsetX, y1+offsetY, y2+offsetY);
    startMouse = mousePos;
  }.bind(this);

  var dragMouse = function(event) {
    stage.fillStyle = "#FFFFFF";
    stage.fillRect(0, 0, canvas.width, canvas.height);
    mousePos = getMousePos(event);
    var newx1 = x1-((mousePos.x-startMouse.x)/canvas.width)*(x2-x1);
    var newx2 = x2-((mousePos.x-startMouse.x)/canvas.width)*(x2-x1);
    var newy1 = y1+((mousePos.y-startMouse.y)/canvas.height)*(y2-y1);
    var newy2 = y2+((mousePos.y-startMouse.y)/canvas.height)*(y2-y1);

    //If it's been dragged far enough, recalculate the line
    if (Math.abs(mousePos.x-startMouse.x)>canvas.width*0.2 || Math.abs(mousePos.y-startMouse.y)>canvas.height*0.2) {
      redrawLine();

    //Otherwise, move around the drawing we already have
    } else {
      drawAxes(newx1, newx2, newy1, newy2);
      stage.drawImage(graphCanvas, mousePos.x-startMouse.x, mousePos.y-startMouse.y);
    }

    if (event.preventDefault) event.preventDefault();
    return false;
    
  }.bind(this);

  //Stops dragging, resets listeners
  var endDrag = function(event) {
    document.removeEventListener("mousemove", dragMouse, false);
    document.removeEventListener("mouseup", endDrag, false);
    document.documentElement.style["-moz-user-select"] = "auto";
    document.documentElement.style["-webkit-user-select"] = "auto";
    document.documentElement.style["-khtml-user-select"] = "auto";
    document.documentElement.style["user-select"] = "auto";
    canvas.addEventListener("mouseover", startMouseOver, false);
    canvas.addEventListener("mousemove", moveMouse, false);
    mousePos = getMousePos(event);

    var offsetX = ((mousePos.x-startMouse.x)/canvas.width)*(x2-x1);
    var offsetY = ((mousePos.y-startMouse.y)/canvas.height)*(y2-y1);
    this.setRange(x1-offsetX, x2-offsetX, y1+offsetY, y2+offsetY);
  }.bind(this);

  var startMouseOver = function(event) {
    canvas.addEventListener("mousemove", moveMouse, false);
    canvas.addEventListener("mouseout", endMouseOver, false);
  }.bind(this);

  //Draws coordinates over point
  var moveMouse = function(event) {
    if (distX===0 && distY===0) {
      stage.fillStyle = "#FFFFFF";
      stage.fillRect(0, 0, canvas.width, canvas.height);
      drawAxes(x1, x2, y1, y2);
      stage.drawImage(graphCanvas, 0, 0);
      mousePos = getMousePos(event);
      if (mousePos.x<0) mousePos.x=0;
      if (mousePos.y<0) mousePos.y=0;
      var offsetY = -y1;

      //Check if the function exists at that x value
      if (points[Math.round(mousePos.x/canvas.width*points.length)].y===0 || points[Math.round(mousePos.x/canvas.width*points.length)].y) {

        //Draw the coordinate
        stage.fillStyle="#2980b9";
        stage.beginPath();
        stage.arc(mousePos.x, canvas.height-((points[Math.round(mousePos.x/canvas.width*points.length)].y+offsetY)/(y2-y1))*canvas.height, 4, 0, 2*Math.PI);
        stage.closePath();
        stage.fill();
        stage.fillStyle="#000";
        stage.strokeStyle="#FFF";
        stage.lineWidth=4;
        stage.textBaseline="alphabetic";
        var txt="(" + (Math.round(points[Math.round(mousePos.x/canvas.width*points.length)].x*100)/100).toFixed(2) + ", " + (Math.round(points[Math.round(mousePos.x/canvas.width*points.length)].y*100)/100).toFixed(2) + ")";

        if (mousePos.x<stage.measureText(txt).width/2+2) {
          stage.textAlign = "left";
        } else if (mousePos.x>canvas.width-stage.measureText(txt).width/2-2) {
          stage.textAlign = "right";
        } else {
          stage.textAlign = "center";
        }
        stage.strokeText(txt, mousePos.x, -10+canvas.height-((points[Math.round(mousePos.x/canvas.width*points.length)].y+offsetY)/(y2-y1))*canvas.height);
        stage.fillText(txt, mousePos.x, -10+canvas.height-((points[Math.round(mousePos.x/canvas.width*points.length)].y+offsetY)/(y2-y1))*canvas.height);
      }
    }
  }.bind(this);

  var endMouseOver = function(event) {
    canvas.removeEventListener("mousemove", moveMouse, false);
    canvas.removeEventListener("mouseout", endMouseOver, false);
    stage.fillStyle = "#FFFFFF";
    stage.fillRect(0, 0, canvas.width, canvas.height);
    drawAxes(x1, x2, y1, y2);
    stage.drawImage(graphCanvas, 0, 0);
  }.bind(this);

  //Zooms based on scroll wheel
  var scrollZoom = function(event) {
    var delta = Math.max(-1, Math.min(1, (event.wheelDelta || -event.detail)));
    distX += delta*(x2-2*distX-x1)/25;
    distY += delta*(y2-2*distY-y1)/25;
    stage.fillStyle = "#FFFFFF";
    stage.fillRect(0, 0, canvas.width, canvas.height);
    drawAxes(x1 + distX, x2 - distX, y1 + distY, y2 - distY);
    stage.drawImage(graphCanvas, canvas.width*(1-((x2-x1)/(x2-2*distX-x1)))/2, canvas.height*(1-((y2-y1)/(y2-2*distY-y1)))/2, canvas.width*((x2-x1)/(x2-2*distX-x1)), canvas.height*((y2-y1)/(y2-2*distY-y1)));
    if (event.preventDefault) event.preventDefault();
    clearTimeout(timer);
    timer = setTimeout(updateZoom, 50);
    return false;
  }.bind(this);

  var updateZoom = function() {
    stage.fillStyle = "#FFFFFF";
    stage.fillRect(0, 0, canvas.width, canvas.height);
    this.setRange(x1 + distX, x2 - distX, y1 + distY, y2 - distY);
    distX=0;
    distY=0;
    clearTimeout(timer);
  }.bind(this);

  //Returns the canvas element
  this.getCanvas = function() {
    return canvas;
  };

  this.getX1 = function() {
    return x1;
  };

  this.getX2 = function() {
    return x2;
  };

  this.getY1 = function() {
    return y1;
  };

  this.getY2= function() {
    return y2;
  };

  //If canvas drawing is supported
  if (canvas.getContext) {

    //Get the canvas context to draw onto
    stage = canvas.getContext("2d");
    stage.font = "12px sans-serif";
    canvas.style.backgroundColor="#FFF";

    graphStage = graphCanvas.getContext("2d");

    //Make points
    this.update();

    canvas.addEventListener("mousedown", startDrag, false);
    canvas.addEventListener("mouseover", startMouseOver, false);
    canvas.addEventListener("mousewheel", scrollZoom, false);
    canvas.addEventListener("DOMMouseScroll", scrollZoom, false);
  } else {
    XCalc.log("Canvas not supported in this browser.");
    canvas = document.createElement("div");
    canvas.innerHTML="Canvas is not supported in this browser.";
  }
}

//Module for input checking and parsing
var XCalc = (function() {
  var worker={};

  worker.errors=[];

  //logs errors
  worker.log = function(message) {
    this.errors.push(message);
  };

  worker.clearErrors = function() {
    this.errors = [];
  };

  worker.hasErrors = function() {
    return this.errors.length;
  };

  //creates a list of errors to be displayed
  worker.displayErrors = function() {
    var errorDiv = document.createElement("div");
    errorDiv.className="error";
    errorDiv.innerHTML = "Errors:";
    var errorList = document.createElement("ul");
    for (var i=0; i<this.errors.length; i++) {
      var e = document.createElement("li");
      e.innerHTML = this.errors[i];
      errorList.appendChild(e);
    }
    errorDiv.appendChild(errorList);
    return errorDiv;
  };

  //Checks to see if brackets are properly nested in a string
  worker.properBrackets = function(value) {
    var openBrackets=0;
    for (var i=0; i<value.length; i++) {
      if (value.substr(i, 1)=="(") openBrackets++;
      if (value.substr(i, 1)==")") openBrackets--;
    }
    return openBrackets===0;
  };

  //Creates a new Segment for an expression
  worker.createExpression = function(value) {
    if (this.properBrackets(value)) {
      return new Segment(value);
    } else {
      this.log("Improperly nested brackets.");
      return 0;
    }
  };

  //Creates a new Graph for an expression
  worker.graphExpression = function(value, width, height, x1, x2, y1, y2) {
    if (this.properBrackets(value)) {
      return new Graph(value, width, height, x1, x2, y1, y2);
    } else {
      this.log("Improperly nested brackets.");
      return 0;
    }
  };

  return worker;
}());



function simplifyText(event) {

  //Grabs data from input elements
  var input = document.getElementById("input").value;
  var x1 = (document.getElementById("x1").value==="")?undefined:parseFloat(document.getElementById("x1").value);
  var x2 = (document.getElementById("x2").value==="")?undefined:parseFloat(document.getElementById("x2").value);
  var y1 = document.getElementById("y1").value?(document.getElementById("y1").value.trim()=="auto")?"auto":parseFloat(document.getElementById("y1").value):undefined;
  var y2 = document.getElementById("y2").value?(document.getElementById("y2").value.trim()=="auto")?"auto":parseFloat(document.getElementById("y2").value):undefined;

  var derive = false;
  if (input.lastIndexOf("derive")!=-1) {
    derive=true;
    input = input.substring(input.lastIndexOf("derive")+6);
  } else if (input.lastIndexOf("derivative of")!=-1) {
    derive=true;
    input = input.substring(input.lastIndexOf("derivative of")+13);
  } else if (input.lastIndexOf("derivative")!=-1) {
    derive=true;
    input = input.substring(input.lastIndexOf("derivative")+10);
  } else if (input.lastIndexOf("dy/dx")!=-1) {
    derive=true;
    input = input.substring(input.lastIndexOf("dy/dx")+5);
  } else if (input.lastIndexOf("d/dx")!=-1) {
    derive=true;
    input = input.substring(input.lastIndexOf("d/dx")+4);
  }

  //Makes the results pane close
  document.getElementById("wrapper").className="";

  //wait for pane to close
  var timer = setTimeout(function() {
    var width=500;
    if (document.getElementById("wrapper").offsetWidth<550) width = document.getElementById("wrapper").offsetWidth - 50;

    document.getElementById("result").innerHTML = "";

    var inputFunction = XCalc.createExpression(input);
    var graph;
    var derivative;
    var derivativeGraph;

    if (derive) {
      derivative = inputFunction.derive();
      derivativeGraph = XCalc.graphExpression(derivative, width, Math.round(width*0.4), x1, x2, y1, y2);
      graph = XCalc.graphExpression(inputFunction, width, Math.round(width*0.5), x1, x2, y1, y2);
    } else {
      graph = XCalc.graphExpression(inputFunction, width, Math.round(width*0.8), x1, x2, y1, y2);
    }

    //If there are no errors, show the graph
    if (!XCalc.hasErrors()) {
      if (derive) {
        var derivativeFormula = document.createElement("div");
        derivativeFormula.className = "formula";
        derivativeFormula.innerHTML = "y' = " + derivative.prettyFormula();
        document.getElementById("result").appendChild(derivativeFormula);
        document.getElementById("result").appendChild(derivativeGraph.getCanvas());
      }
      var inputFormula = document.createElement("div");
      inputFormula.className = "formula";
      inputFormula.innerHTML = "y = " + inputFunction.simplify().prettyFormula();
      document.getElementById("result").appendChild(inputFormula);
      document.getElementById("result").appendChild(graph.getCanvas());
      document.getElementById("wrapper").className="open";

    //Otherwise, show the errors, then clear the error list
    } else {
      document.getElementById("result").appendChild(XCalc.displayErrors());
      document.getElementById("wrapper").className="open";
      XCalc.clearErrors();
    }
  }, 800);
}

function onKeyUp(event) {
  if (event.keyCode==13) {
    simplifyText();
  }
}

window.onload = function() {
  document.getElementById("graph").addEventListener("click", simplifyText);
  document.getElementById("input").addEventListener("keyup", onKeyUp);
  simplifyText();
};
              
            
!
999px

Console