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Differentiable off and even functions 
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#1
Sep1310, 08:38 AM

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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. 


#2
Sep1310, 08:44 AM

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



#3
Sep1310, 09:06 AM

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Thanks
PF Gold
P: 39,568

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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