# 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.
 Mentor P: 4,225 Why don't you show us what you did? It might help to change h to -h in the limit definition
 PF Patron Sci Advisor Thanks Emeritus P: 38,430 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.

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