A Survey on the (Hyper-) Derivatives in Complex, Quaternionic and Clifford Analysis

The complex derivative serves as one of the definitions for holomorphic functions but also as an important characteristic of the latter having algebraic, topologic and analytic aspects. The goal of the paper is to explain that in the framework of quaternionic and Clifford analyses there exists the hyperderivative of a hyperholomorphic function which extends to the corresponding situations a series of fundamental properties of its complex antecedent.