Derivative of Power of Function

Theorem
Let $\map u x$ be a differentiable real function of $x$.

Let $n$ be a real number such that $n \ne -1$.

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

Also presented as
This can be (and usually is) presented more simply as:


 * $\map {\dfrac \d {\d x} } {u^n} = n u^{n - 1} \dfrac {\d u} {\d x}$