This book is aimed at first-year students and scholars of Higher Education Institutions. It contains all the knowledge about derivatives that is not taught in high school but is essential for students. However, it also systematizes many of the knowledge from high school.

The study of derivatives begins with the definition and the rules of differentiation. Here, emphasis is placed on the differentiation of the inverse function, particularly the inverses of trigonometric functions (circular functions). Based on this, the differentiation of functions presented in (parametric) and in parametric form is examined.

In the chapter on theorems of derivatives, emphasis is given to the proof of inequality relations, the Taylor theorem, and its applications. Subsequently, indeterminate forms are studied with the help of L'Hospital's rule. Finally, the graphical representation of functions is presented in the form y:f (x) and in the form r:r (φ).

Special effort has been made for a as simple as possible presentation of the various topics, so that the reader can understand the corresponding concepts and techniques as quickly as possible.

GAROUTSOS YANNIS [Excerpt from the text of the preface]