# Prove that the derivative of an odd function is even

1. Dec 1, 2011

### NWeid1

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. Dec 1, 2011

### 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.

3. Dec 2, 2011

### HallsofIvy

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