The original poster questions whether the composition of two differentiable functions is always differentiable, providing examples of specific functions to illustrate the inquiry.
There is an ongoing exploration of the differentiability of function compositions, with participants offering insights into notation and the application of the chain rule. No explicit consensus has been reached regarding the original question.
Participants note the importance of precise mathematical notation when discussing function composition, indicating a potential misunderstanding in the original post regarding the representation of functions.
Sure. You even know a formula for the derivative, right?
I'll just comment about one of my little pet peeves. h(k(x)) is a number, not a function. The function you have in mind is written as LaTeX Code: h\\circ k or LaTeX Code: x\\mapsto h(k(x)) . (Note the special "mapsto" arrow).