Derivative of Logarithm Function

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

Then $$D_x \left({\ln x}\right) = \frac 1 x$$.

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

Then $$D_x \left({\log_a x}\right) = \frac {\log_a e} x$$.

Proof for Natural Logarithm
Follows directly from the definition of the natural logarithm function as the primitive of the reciprocal function.