Numerical differentiation is the process of finding the numerical value of a derivative of a given function at a given point. In general, numerical differentiation is more
difficult than numerical integration. This
is because while numerical integration requires
only good continuity properties of the function being integrated, numerical differentiation
requires more complicated properties such as Lipschitz classes. Numerical differentiation
is implemented as ND[f,
x, x0, Scale -> scale] in the Wolfram
Language package NumericalCalculus` .

There are many applications where derivatives need to be computed numerically. The
simplest approach simply uses the definition of the derivative