Partial Differentiation

This lecture covers simple examples of partial differentiation, where the instructor explains the process of treating other variables as constants and differentiating with respect to a single variable. Through various examples in two dimensions, the lecture demonstrates how to calculate partial derivatives and gradients, emphasizing the importance of treating each variable separately. The instructor also explores the concept of symmetric matrices and how to calculate partial derivatives in different scenarios, including points where functions are not continuous. The lecture concludes with a detailed explanation of the composition of functions and the gradient of a function in terms of its partial derivatives.