I was wondering if someone would be able to help me understand how to approach this question, as I'm unsure what it's saying.
The question is:
You are given a differentiable function $f$ : $R \to R$ which satisfies the equality, $$f(\exp(f(x))=f(x)$$
for all $x \in R$. Show that if $f'(x)$ doesn't equal 0, then
$$f'(\exp(f(x)))=\exp(-f(x))$$
Note: This is meant to be $e$ to the power of $f(x)$ on the LHS, but I can't get it to write that, and $e$ to the power of $-f(x)$ on the RHS.
Any help with this questions would be most appreciated. Thank you.