Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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. :)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook