Differential Functions: Derivability and Gradient

This lecture covers the concept of differentiability in functions of single and multiple variables, discussing the existence of partial derivatives, directional derivatives, and gradients. The instructor explains the comparison between the derivability of functions with one variable and functions with multiple variables, emphasizing the conditions for a function to be differentiable. The lecture also delves into the significance of gradients in determining the direction of the largest directional derivative. Various theorems related to differentiability and the existence of derivatives are presented, providing a comprehensive understanding of differential functions.