Derivatives and Tangent Planes

This lecture covers the concept of derivatives for functions of one and two variables, including the definition of derivative, differentiability, and tangent planes. It also explores the existence of partial derivatives and the continuity of functions. The instructor discusses the linear approximation of functions around a point and the conditions for a function to be differentiable. The lecture concludes with a detailed explanation of tangent planes to the graph of a function at a given point.