Derivative of Logarithm Function

Theorem

Natural Logarithm

Let $\ln x$ be the natural logarithm function.

Then:

$\map {\dfrac \d {\d x} } {\ln x} = \dfrac 1 x$

General Logarithm

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

Let $\log_a x$ be the logarithm function to base $a$.

Then:

$\map {\dfrac \d {\d x} } {\log_a x} = \dfrac {\log_a e} x$