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Differentiable off and even functions

by tsang
Tags: differentiable, functions
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tsang
#1
Sep13-10, 08:38 AM
P: 15
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.
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Office_Shredder
#2
Sep13-10, 08:44 AM
Emeritus
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PF Gold
P: 4,500
Why don't you show us what you did? It might help to change h to -h in the limit definition
HallsofIvy
#3
Sep13-10, 09:06 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,363
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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