Question

Fill in the blank:

$\frac{d}{dx}\left(\ln \left|x\right|\right)=---$

Short answer

$\frac{d}{dx}\left(\ln \left|x\right|\right)=\frac{1}{\left|x\right|}$

Step-by-step solution

Given Information

The given expression is$\frac{d}{dx}\left(\ln \left|x\right|\right)$

Simplification

We know that $\frac{d}{dx}\left(\ln \left(x\right)\right)=\frac{1}{x}$

width="136" height="41" role="math">⇒ddxlnx=1x

$=\frac{1}{x},x>0$

$=\frac{1}{\left|x\right|},x<0$