Directional Derivatives

This lecture delves into the concept of directional derivatives, emphasizing the importance of differentiability and the existence of gradients. Through detailed examples, the instructor illustrates how to calculate directional derivatives and highlights scenarios where directional derivatives exist but the function is not differentiable, showcasing the intricacies of functions at the origin. By exploring various approaches, such as polar coordinates and gradient calculations, the lecture provides a comprehensive understanding of directional derivatives and their implications.