/pre>
<p>
      This requests a second-order accurate derivative be computed.
    </p>
<p>
      It is emphatically <span class="emphasis"><em>not</em></span> the case that higher order methods
      always give higher accuracy for smooth functions. Higher order methods require
      more addition of positive and negative terms, which can lead to catastrophic
      cancellation. A function which is very good at making a mockery of finite-difference
      differentiation is exp(x)/(cos(x)<sup>3</sup> + sin(x