Differentiability Analysis

This lecture covers the analysis of differentiability in functions, focusing on partial derivatives, Schwarz's theorem, and the existence and continuity of functions. It explores the concept of directional slopes and the rules for deriving functions. The instructor discusses the conditions for differentiability and continuity, emphasizing the importance of open sets and the direction of slopes. Schwarz's theorem is highlighted as a key concept in understanding the existence and continuity of functions.