If $f$ is of given parity, what can be said of its derivative and primitive? If $f$ is of given parity, what can be said of it's derivative and primitive? Clearly for power functions or simple trigonometric functions it seems that the parity of the derivative and antiderivative are opposite to that of the function itself. But is this true in general? If so, how to prove/disprove it?

Hint:
$$f'(-x) = \lim_{h\to 0}\frac{f(-x-h)-f(-x)}{h}.$$
