Differentiable off and even functions

[tsang]

Homework Statement

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.

Homework Equations

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.

 

[Office_Shredder]

Why don't you show us what you did? It might help to change h to -h in the limit definition

 

[HallsofIvy]

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.