# Differentiable off and even functions

1. ### tsang

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.

2. ### Office_Shredder

4,500
Staff Emeritus
Why don't you show us what you did? It might help to change h to -h in the limit definition

3. ### HallsofIvy

40,308
Staff Emeritus
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.