Question

I m writing a piece of client-side javascript code that takes a function and finds the derivative of it, however, the regex that s supposed to match with the power rule fails to work in the context of the javascript program, even though it sucessfully matches when it s used with an independent regex tester.

The code is extremely bare-bones at the moment, and I m planning to flesh it out later.

The browser I m executing this on is Midori, and the operating system is Ubuntu 10.04 (Lucid Lynx). Here s the HTML page being used as the interface in addition to the code:

Page:

<html>
  <head>
    <title>
      Derivative Calculator
    </title>
    <script type="text/javascript" src="derivative.js">
    </script>
    <body>
      <form action="" name=form>
  <input type=text name=f /> with respects to
  <input type=text name=vr size=7 />
  <input type=button value="Derive!" onClick="main(this.form)" /> <br />
  <input type=text name=result value="" />
      </form>
   </body>
</html>

derivative.js:

function main(form) {
    form.result.value = derive(form.f.value, form.vr.value);
}

function derive(f, v) {
    var atom = [];
    atom["sin(" + v + ")"] = "cos(" + v + ")";
    atom["cos(" + v + ")"] = "-sin(" + v + ")";
    atom["tan(" + v + ")"] = "sec^(2)(" + v + ")";
    atom["sec(" + v + ")"] = "sec(" + v + ")*tan(" + v + ")";
    atom["1/(cos(" + v + "))"] = "sec(" + v + ")*tan(" + v + ")";
    atom["csc(" + v + ")"] = "-csc(" + v + ")*cot(" + v + ")";
    atom["1/(sin(" + v + "))"] = "-csc(" + v + ")*cot(" + v + ")";
    atom["cot(" + v + ")"] = "-csc^(2)(" + v + ")";
    atom["1/(tan(" + v + "))"] = "-csc^(2)(" + v + ")";
    atom["sin^(-1)(" + v + ")"] = "1/sqrt(1 - " + v + "^(2))";
    atom["arcsin(" + v + ")"] = "1/sqrt(1 - " + v + "^(2))";
    atom["cos^(-1)(" + v + ")"] = "-1/sqrt(1 - " + v + "^(2))";
    atom["arccos(" + v + ")"] = "-1/sqrt(1 - " + v + "^(2))";
    atom["tan^(-1)(" + v + ")"] = "1/(1 + " + v + "^(2))";
    atom["arctan(" + v + ")"] = "1/(1 + " + v + "^(2))";
    atom["sec^(-1)(" + v + ")"] = "1/(|" + v + "|*sqrt(" + v + "^(2) - 1))"; 
    atom["arcsec(" + v + ")"] = "1/(|" + v + "|*sqrt(" + v + "^(2) - 1))"; 
    atom["csc^(-1)(" + v + ")"] = "-1/(|" + v + "|*sqrt(" + v + "^(2) - 1))"; 
    atom["arccsc(" + v + ")"] = "-1/(|" + v + "|*sqrt(" + v + "^(2) - 1))"; 
    atom["cot^(-1)(" + v + ")"] =  "-1/(1 + " + v + "^(2))";
    atom["arccot(" + v + ")"] =  "-1/(1 + " + v + "^(2))";
    atom["ln(" + v + ")"] = "1/(" + v + ")";
    atom["e^(" + v + ")"] = "e^(" + v + ")";
    atom["ln(|" + v + "|)"] = "1/(" + v + ")";
    atom[v] = "1";

    var match = "";
    if (new Boolean(atom[f]) == true) {
        return atom[f];
    } else if (f.match(/^[0-9]+$/)) {
        return "";
    } else if (f.match(/([S]+)([s]+)+([s]+)([S]+)/)) {
        match = /([S]+)([s]+)+([s]+)([S]+)/.exec(f);
        return derive(match[1], v) + " + " + derive(match[4], v);
    } else if (f.match(new RegExp("^([0-9]+)(" + v + ")$"))) {
        match = new RegExp("^([0-9]+)(" + v + ")$").exec(f);
        return match[1];
    } else if (f.match(new RegExp("^([0-9]+)(" + v + ")^([0-9]+)$"))) {
        match = new RegExp("^([0-9]+)(" + v + ")^([0-9]+)$").exec(f);
        return String((match[1] * (match[3]))) + v + "^" +
                   String(match[3] - 1);
    } else {
        return "?";
    }
}

In particular, I m having trouble with this pattern:

    } else if (f.match(new RegExp("^([0-9]+)(" + v + ")^([0-9]+)$"))) {
        match = new RegExp("^([0-9]+)(" + v + ")^([0-9]+)$").exec(f);
        return String((match[1] * (match[3]))) + v + "^" +
                   String(match[3] - 1);

Answer 1

You need to double-escape your caret:

")\^([0-9]+)$"

Otherwise javascript doesn t interpret the backslash as a backslash, and therefore never escapes the caret for the regex.

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