The Chain Rule

In this video we discuss the Chain Rule and its formulation and relationship to the Jacobian matrix. We start by introducing the concept of composite functions and examine how they can be used to calculate the derivative of a simple scalar function. We then extend this idea to vector valued functions and demonstrate how the Chain Rule is related to the gradient/Jacobian of a function Topics and timestamps: 0:00 – Introduction 4:06 – Single input single output function 16:26 – Multiple input single output function 19:52 – Formulation as a composite function 36:25 – Relationship to Jacobian matrix 40:05 – Multiple input multiple output function Lecture notes and code can be downloaded from https://github.com/clum/YouTube/tree/main/Calculus14 All Calculus videos in a single playlist (https://www.youtube.com/playlist?list=PLxdnSsBqCrrGHwNWnP5XVhytcGL9ExuPE) #Calculus You can support this channel via Patreon at https://www.patreon.com/christopherwlum or by clicking on the ‘Thanks’ button underneath the video. Thank you for your help!