Power Rule for Derivatives/Corollary

Corollary to Power Rule for Derivatives
Let $n \in \R$.

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

Then:
 * $\map {\dfrac \d {\d x} } {c x^n} = n c x^{n - 1}$

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