Numerical Derivative

While it is usually much easier to compute a Derivative instead of an Integral (which is a little strange, considering that ``more'' functions have integrals than derivatives), there are still many applications where derivatives need to be computed numerically. The simplest approach simply uses the definition of the Derivative

$$f'(x)\equiv \lim_{h\to 0}{f(x+h)-f(x)\over h}$$

for some small numerical value of $h\ll 1$.

See also Numerical Integration

References

Numerical Methods

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Numerical Derivatives.'' §5.7 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 180-184, 1992.