Derivative of General Logarithm Function/Also presented as

Derivative of General Logarithm Function: Also presented as

This result can also be seen presented as:

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

where $\ln a := \log_e a$ is the natural logarithm of $a$.

This is seen to be equivalent to the given form by Logarithm of Reciprocal:

$\dfrac 1 {\ln a} = \log_a e$

Sources

• 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text {II}$. Calculus: Differentiation: Log to base $a$