1. The problem statement, all variables and given/known data Let f: R[tex]\rightarrow[/tex] 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.
Are you using the difference quotient? You should be able to do this by differentiating f'(-x), letting u= -x and using the chain rule.