# Derivate of an odd function

1. Dec 5, 2004

### Zaare

It seems the derivate of an odd function $$(f(-x)=-f(x))$$ is an even function $$(f(-x)=f(x))$$, and vice versa. Is there a theroem about this?

2. Dec 5, 2004

### Muzza

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.

3. Dec 5, 2004

### Zaare

Ah, that was easy. Thank you. :)