GNU Scientific Library – Reference Manual: Numerical Differentiation Examples

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### 29.2 Examples

The following code estimates the derivative of the function 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 `gsl_deriv_forward`.

    #include <stdio.h>
    #include <gsl/gsl_math.h>
    #include <gsl/gsl_deriv.h>

    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 = &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;
    }

Here is the output of the program,

    $ ./a.out

    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