Power Rule for Derivatives/Fractional Index

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

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

Then:
 * $f' \left({x}\right) = n x^{n-1}$

everywhere that $f \left({x}\right) = x^n$ is defined.

When $x = 0$ and $n = 0$, $f' \left({x}\right)$ is undefined.