tion
        are rather hard to work out by hand, but fortunately <a href="http://www.wolframalpha.com/input/?i=d%2Fda+%5b4+*+a+*+EllipticE%281+-+b%5e2%2Fa%5e2%29%5d" target="_top">Wolfram
        Alpha</a> can do the grunt work for us to give:
      </p>
<pre class="programlisting">d/da L(a, b) = 4(a<sup>2</sup>E(k) - b<sup>2</sup>K(k)) / (a<sup>2</sup> - b<sup>2</sup>)</pre>
<p>
        Note that now we have <span class="bold"><strong>two</strong></span> elliptic integral
        calls to get the derivati