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Derivate of an odd function

  1. Dec 5, 2004 #1
    It seems the derivate of an odd function [tex](f(-x)=-f(x))[/tex] is an even function [tex](f(-x)=f(x))[/tex], and vice versa. Is there a theroem about this?
     
  2. jcsd
  3. Dec 5, 2004 #2
    Suppose f is odd. We have that (f(-x))' = (-f(x))' = -f'(x). But by the chain rule, (f(-x))' = -f'(-x). Thus -f'(-x) = -f'(x) <=> f'(-x) = f'(x) <=> f' is even.
     
  4. Dec 5, 2004 #3
    Ah, that was easy. Thank you. :)
     
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