Jürgen Beetz first introduces the origins of the imagined stories of mathematics from the Stone Age. He then presents the central question of calculus using a simple example. The author explains the fundamental problem of differentiation: determining the slope, that is, the direction of the tangent, at any point of a function y=f(x). As practical examples of differentiation, he discusses the hyperbola and the sine function. Jürgen Beetz dedicates a separate chapter to the peculiarities of the exponential function.