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 $f \left({x}\right) = x^n$.

Then:
 * $\dfrac {\mathrm d}{\mathrm d x} \left({c x^n}\right) = n c x^{n-1}$

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

Proof
Follows from Power Rule for Derivatives, and Derivative of Constant Multiple.