# How do you graph the derivative of f(x) = log (x)?

Dec 22, 2017

See below.

#### Explanation:

First we need to find the derivative of $f \left(x\right) = \log \left(x\right)$

$\frac{d}{\mathrm{dx}} \left(\log \left(x\right)\right) = \frac{1}{x}$

as $x \to {0}^{-} \textcolor{w h i t e}{88888}$ ,$\frac{1}{x} \to - \infty$

as $x \to {0}^{+} \textcolor{w h i t e}{888}$ , $\frac{1}{x} \to \infty$

The y axis is a vertical asymptote.

as $x \to \infty \textcolor{w h i t e}{88888}$ ,$\frac{1}{x} \to 0$

as $x \to - \infty \textcolor{w h i t e}{888}$ ,$\frac{1}{x} \to 0$

The x axis is a horizontal asymptote.

GRAPH:

graph{y=1/x [-16.02, 16.01, -8.01, 8.01]}