Derivative of Logarithm Function
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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:
- $\map {\dfrac \d {\d x} } {\log_a x} = \dfrac {\log_a e} x$