Partial Derivatives: Definitions and Applications

This lecture covers the definitions and applications of partial derivatives in functions of several variables, emphasizing the importance of specifying the choice of variables. It explains the concept of partial derivatives as the derivative with respect to one variable while keeping others constant. The lecture also delves into the explicit definition for the case of two variables, illustrating the gradient and its graphical representation. Additionally, it discusses the notion of gradient in differentiable functions and provides equivalent notations for better understanding.