This lecture focuses on the study of derivable functions, starting with the discussion on the derivability of composite functions and the concept of chain rule. It covers the continuity of the derivative function, the derivability of reciprocal functions, and introduces the main tools for the topic: Rolle's theorem and the mean value theorem. The chapter concludes with the reformulation of the mean value theorem as a corollary, which allows for the analysis of functions using properties of derivative functions.