Partial Derivatives and Differentiability

This lecture covers the concept of partial derivatives and differentiability, illustrating through examples the importance of existence of partial derivatives for ensuring differentiability. The lecture also discusses the conditions required for a function to be differentiable at a point, emphasizing the role of continuity. Various methods for verifying differentiability are presented, including the use of polar coordinates. The instructor, Peter Wittwer, demonstrates how to calculate partial derivatives and highlights the significance of the reciprocal theorem in determining differentiability.