Power Rule for Derivatives/Fractional Index

Theorem
Let $n \in \N_{>0}$.

Let $f: \R \to \R$ be the real function defined as $\map f x = x^{1 / n}$.

Then:
 * $\map {f'} x = n x^{n - 1}$

everywhere that $\map f x = x^n$ is defined.

When $x = 0$ and $n = 0$, $\map {f'} x$ is undefined.