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This lecture covers the concept of derivatives of composite functions, focusing on the chain rule theorem. It explains the conditions under which the composition of functions is well-defined and how to calculate the derivative of composite functions. The lecture also discusses the application of linear transformations and matrix multiplication in the context of derivatives. The demonstration of the concepts is based on examples and notation clarification. The lecture concludes with a detailed explanation of the derivative calculation process and the importance of understanding the chain rule in function composition.