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<title>Numerical Differentiation Examples - GNU Scientific Library -- Reference Manual</title>
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<h3 class="section">27.2 Examples</h3>
<p>The following code estimates the derivative of the function
<!-- {$f(x) = x^{3/2}$} -->
f(x) = x^{3/2}
at x=2 and at x=0. The function f(x) is
undefined for x<0 so the derivative at x=0 is computed
using <code>gsl_deriv_forward</code>.
<pre class="example"><pre class="verbatim"> #include <stdio.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_deriv.h>
double f (double x, void * params)
{
return pow (x, 1.5);
}
int
main (void)
{
gsl_function F;
double result, abserr;
F.function = &f;
F.params = 0;
printf ("f(x) = x^(3/2)\n");
gsl_deriv_central (&F, 2.0, 1e-8, &result, &abserr);
printf ("x = 2.0\n");
printf ("f'(x) = %.10f +/- %.10f\n", result, abserr);
printf ("exact = %.10f\n\n", 1.5 * sqrt(2.0));
gsl_deriv_forward (&F, 0.0, 1e-8, &result, &abserr);
printf ("x = 0.0\n");
printf ("f'(x) = %.10f +/- %.10f\n", result, abserr);
printf ("exact = %.10f\n", 0.0);
return 0;
}
</pre></pre>
<p class="noindent">Here is the output of the program,
<pre class="example"> $ ./a.out
<pre class="verbatim"> f(x) = x^(3/2)
x = 2.0
f'(x) = 2.1213203120 +/- 0.0000004064
exact = 2.1213203436
x = 0.0
f'(x) = 0.0000000160 +/- 0.0000000339
exact = 0.0000000000
</pre></pre>
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