Derivatives and integrals are the tools of analysis. The chapter begins with an introduction to the differential calculus of complex-valued functions, which are defined on suitable subsets of \({\mathbb{K}}\) . This sets a common path from the beginning into both the real and the complex world of differentiable functions. The central position of the complex exponential function is thereby—once again—clearly demonstrated, and in corresponding attire, central results such as the boundary theorem also appear. In addition, there is a first impression of power series and their significance as germs of analytic functions.