Differentiability in Analysis

This lecture covers the concept of differentiability in analysis, focusing on the conditions for a function to be differentiable. Starting with the definition and existence of partial derivatives, it progresses to the criteria for differentiability and continuity. Through examples and propositions, the instructor demonstrates how to determine if a function is differentiable and continuous at a given point. The lecture concludes with a detailed explanation of differentiability in R² and the role of partial derivatives in establishing continuity. Various proofs and calculations are provided to illustrate the concepts discussed.