Implicit functions theorem

This lecture covers the implicit functions theorem, focusing on the concept of implicit differentiation and its applications in defining functions implicitly. The instructor explains the theorem through various examples, demonstrating how to determine the differentiability of functions and their derivatives. The lecture also delves into the derivation of implicit functions, showcasing the process of finding derivatives and evaluating them at specific points. Additionally, the presentation explores the conditions under which functions are locally differentiable and the implications of the theorem in the context of continuous functions.