This lecture covers the representation of differentiable functions in R², focusing on graphical representations and vector interpretations. It also delves into the concept of local copies of R² and the interpretation of images as vectors in this context. The lecture further explores the graphical representation of differentiable functions and the concept of changes of coordinates through bijections. The derivability of reciprocal functions is discussed, emphasizing the importance of understanding vector interpretations and graphical representations in the context of differentiable functions.