Derivative of General Logarithm of Function

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

Let $a \in \R_{>0}$ such that $a \ne 1$

Let $\log_a u$ be the logarithm to base $a$ of $u$.

Then:
 * $\map {\dfrac \d {\d x} } {\log_a u} = \dfrac {\log_a e} u \dfrac {\d u} {\d x}$