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Prove that the derivative of an odd function is even

  1. Dec 1, 2011 #1
    A function f is an even function is f(-x)=f(x) for all x and is an odd function is f(-x)=-f(x) for all x. Prove that the derivative of an odd function is even and the derivative of an even function is off. I get what even and odd functions are but I'm not sure how to rigorously prove this. Thanks.
     
  2. jcsd
  3. Dec 1, 2011 #2

    Mark44

    Staff: Mentor

    One way to do this is to use the limit definition of the derivative.

    PS - don't delete the parts of the posting template.
     
  4. Dec 2, 2011 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Or, and I think simpler, use the chain rule to differentiate f(-x) with respect to x.
     
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