Numerical differentiation: A challenging problem

To some people, numerical differentiation sounds a trivial task, which can be easily done by difference formulas. However, cancellation is a serious problem with these formulas, especially the ones for higher order derivatives. In order to solve this problem, the complex calculus is usually employed. There are two main approaches, and the aim of this article is to give a brief review of them: These are complex step differentiation formulas, and the Cauchy integral approach