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<title>GNU Scientific Library &ndash; Reference Manual: Numerical Differentiation Examples</title>

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<a name="Numerical-Differentiation-Examples"></a>
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<p>
Next: <a href="Numerical-Differentiation-References.html#Numerical-Differentiation-References" accesskey="n" rel="next">Numerical Differentiation References</a>, Previous: <a href="Numerical-Differentiation-functions.html#Numerical-Differentiation-functions" accesskey="p" rel="previous">Numerical Differentiation functions</a>, Up: <a href="Numerical-Differentiation.html#Numerical-Differentiation" accesskey="u" rel="up">Numerical Differentiation</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<hr>
<a name="Examples-20"></a>
<h3 class="section">29.2 Examples</h3>

<p>The following code estimates the derivative of the function 
<em>f(x) = x^{3/2}</em> 
at <em>x=2</em> and at <em>x=0</em>.  The function <em>f(x)</em> is
undefined for <em>x&lt;0</em> so the derivative at <em>x=0</em> is computed
using <code>gsl_deriv_forward</code>.
</p>
<div class="example">
<pre class="verbatim">#include &lt;stdio.h&gt;
#include &lt;gsl/gsl_math.h&gt;
#include &lt;gsl/gsl_deriv.h&gt;

double f (double x, void * params)
{
  (void)(params); /* avoid unused parameter warning */
  return pow (x, 1.5);
}

int
main (void)
{
  gsl_function F;
  double result, abserr;

  F.function = &amp;f;
  F.params = 0;

  printf (&quot;f(x) = x^(3/2)\n&quot;);

  gsl_deriv_central (&amp;F, 2.0, 1e-8, &amp;result, &amp;abserr);
  printf (&quot;x = 2.0\n&quot;);
  printf (&quot;f'(x) = %.10f +/- %.10f\n&quot;, result, abserr);
  printf (&quot;exact = %.10f\n\n&quot;, 1.5 * sqrt(2.0));

  gsl_deriv_forward (&amp;F, 0.0, 1e-8, &amp;result, &amp;abserr);
  printf (&quot;x = 0.0\n&quot;);
  printf (&quot;f'(x) = %.10f +/- %.10f\n&quot;, result, abserr);
  printf (&quot;exact = %.10f\n&quot;, 0.0);

  return 0;
}
</pre></div>

<p>Here is the output of the program,
</p>
<div class="example">
<pre class="example">$ ./a.out
</pre><pre class="verbatim">f(x) = x^(3/2)
x = 2.0
f'(x) = 2.1213203120 +/- 0.0000005006
exact = 2.1213203436

x = 0.0
f'(x) = 0.0000000160 +/- 0.0000000339
exact = 0.0000000000
</pre></div>




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