Compute the derivative of log_x e

by RoRi

November 3, 2015

Compute the derivative of the function

$\log_x e.$

(Where $\log_x$ is the base $x$ logarithm.)

First, we rewrite the function in terms of the natural logarithm, $\log$ ,

$f(x) = \log_x e = \frac{\log e}{\log x} = \frac{1}{\log x}.$

Then we take the derivative,

$f'(x) = \frac{-\frac{1}{x}}{(\log x)^2} = \frac{-1}{x (\log x)^2}.$

Stumbling Robot