Differentiable off and even functions

  1. 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. jcsd
  3. Office_Shredder

    Office_Shredder 4,499
    Staff Emeritus
    Science Advisor
    Gold Member

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

    HallsofIvy 40,504
    Staff Emeritus
    Science Advisor

    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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