Partial Derivatives: Functions and Definitions

This lecture covers the concept of partial derivatives, focusing on functions of several variables compared to a single variable. It explains how partial derivatives are derived from a function of several variables, with examples illustrating the process. The lecture also delves into the geometric interpretation of partial derivatives and the existence of derivatives. Emphasis is placed on the definition and properties of partial derivative functions, highlighting their behavior on R². The instructor discusses the continuity of functions and the conditions under which partial derivative functions are well-defined. Various examples and notations are used to clarify the concepts presented.