Question

Prove that the derivative of an odd function is an even function.

Answer 1

Power rule.
Proof:
Where 2n is the counting function of even numbers and
Where 2n-1 is the counting function of odd numbers

\[f(x)=x^{(2n)}\]
\[f'(x)=2nx^{(2n-1)}\]
therefore f'(x) will always be odd if f(x) is even.
QED

Answer 2

n is integer

Answer 3

indeed, thank you for that clarification s martin. This holds IFF n is a real integer.