NAG Library Manual, Mark 28.5
```/* nag_numdiff_fwd (d04aac) Example Program.
*
* Copyright 2022 Numerical Algorithms Group.
*
* Mark 28.5, 2022.
*/

#include <math.h>
#include <nag.h>
#include <stdio.h>

#ifdef __cplusplus
extern "C" {
#endif
static double NAG_CALL f(double x, Nag_Comm *comm);
#ifdef __cplusplus
}
#endif

int main(void) {
/* Scalars */
Integer exit_status = 0;
Integer i, k, l, step, nder;
double hbase, xval;
/* Arrays */
double der, erest, ruser;
double steps = {0.5, 0.05, 0.005, 0.0005};
/* Nag Types */
Nag_Comm comm;
NagError fail;

INIT_FAIL(fail);

printf("nag_numdiff_fwd (d04aac) Example Program Results\n");

/* For communication with user-supplied functions: */
ruser = -1.0;
comm.user = ruser;

/* abs(nder) is largest order derivative required. */
nder = -7;
l = NAG_IABS(nder);
/* nder < 0 and nder is even means only even derivatives,
* and nder < 0 and nder is odd, only odd derivatives.
*/
if (nder < 0) {
step = 2;
} else {
step = 1;
}
/* Derivatives will be evaluated at x = xval. */
xval = 0.5;

printf("\nFour separate runs to calculate the first four odd order "
"derivatives of\n"
"   f(x) = 0.5*exp(2.0*x-1.0) at x = 0.5.\n"
"The exact results are 1, 4, 16 and 64\n\n"
"Input parameters common to all four runs\n"
"  xval = %f     nder = %" NAG_IFMT "\n",
xval, nder);

for (k = 0; k < 4; k++) {
/* nag_numdiff_fwd (d04aac).
* Numerical differentiation, derivatives up to order 14,
* function of one real variable.
*/
hbase = steps[k];
nag_numdiff_fwd(xval, nder, hbase, der, erest, f, &comm, &fail);
if (fail.code != NE_NOERROR) {
printf("Error from nag_numdiff_fwd (d04aac).\n%s\n", fail.message);
exit_status = 1;
goto END;
}

printf("\n"
"with step length %8.4f  the results are\n"
"Order        Derivative       Questionable?\n",
hbase);

for (i = 0; i < l; i += step)
if (erest[i] < 0.0) {
printf("%2" NAG_IFMT " %21s %13s\n", i + 1, "---------", "Yes");
} else {
printf("%2" NAG_IFMT " %21.2e %13s\n", i + 1, der[i], "No");
}
}

END:
return exit_status;
}

static double NAG_CALL f(double x, Nag_Comm *comm) {
if (comm->user == -1.0) {
printf("(User-supplied callback f, first invocation.)\n");
comm->user = 0.0;
}
return 0.5 * exp(2.0 * x - 1.0);
}
```