Differentiable off and even functions

by tsang
Tags: differentiable, functions
 P: 15 1. The problem statement, all variables and given/known data Let f: R$$\rightarrow$$ R be a differentiable even function. Prove that f' is an odd function. Also, prove that if f is a differentiable odd function, then f' is an even function. 2. Relevant equations 3. The attempt at a solution I tried to use definition, so I should tried to prove f'(-x)=-f'(x) for first part, and f'(-x)=f'(x) for second part, but I cannot end up these results.