derivative of even/odd function (proof)

Suppose f(x)=±f(-x). We need to show that f(x)=f(-x). To do this, let us define the auxiliary function m:, m(x)=-x. The condition on f is then f(x)=±(fm)(x). Using the chain ruleMathworldPlanetmath, we have that

f(x) = ±(fm)(x)
= ±f(m(x))m(x)
= f(-x),

and the claim follows.

Title derivative of even/odd functionMathworldPlanetmath (proof)
Canonical name DerivativeOfEvenoddFunctionproof
Date of creation 2013-03-22 13:37:57
Last modified on 2013-03-22 13:37:57
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 5
Author mathcam (2727)
Entry type Proof
Classification msc 26A06