Differentiability and Derivatives

This lecture covers the concept of differentiability and derivatives, including the definition of gof, the differentiability of composite functions, and the theorem of differentiability. It also explores the notion of partial derivatives, the linear approximation, and the theorem of finite increments. The lecture delves into the proof of differentiability, the linear approximation of functions, and the concept of total derivatives. Additionally, it discusses the linearization of functions, the concept of continuity, and the theorem of finite increments. The lecture concludes with a discussion on total derivatives and the theorem of finite increments.