Question

$\frac{d}{dx}\left(\log \left|x\right|\right)=\dots .(x\ne 0)$

• A. $\frac{1}{x}$
• B. $-\frac{1}{x}$
• C. $x$
• D. $-x$

Answer 1

The correct option is A

$\frac{1}{x}$

Finding the value:

Given, $y=\log \left|x\right|\dots .(x\ne 0)$

As we know,

$\left|x\right|=\left\{\begin{array}{ll}x& x\ge 0\\ -x& x<0\end{array}\right.$

But $\log$ is not defined for $x<0$

$\Rightarrow$$\log \left|x\right|=\log x$

Differentiate it with respect to ‘x’, we get

$\therefore \frac{\mathbf{d}\mathbf{\left(}\mathbf{l}\mathbf{o}\mathbf{g}\mathbf{\left|}\mathbf{x}\mathbf{\right|}\mathbf{\right)}}{\mathbf{d}\mathbf{x}}\mathbf{=}\frac{\mathbf{1}}{\mathbf{x}}\mathbf{}$

Hence, option (A) is correct.