Question

If $f\left(x\right)=\log \left|2x\right|,x\ne 0$ then $f^{\prime }\left(x\right)$ is equal to-

• A. $\frac{1}{x}$
• B. $-\frac{1}{x}$
• C. $\frac{1}{\left|x\right|}$
• D. None of these

Answer 1

The correct option is A $\frac{1}{x}$

$f\left(x\right)=\log \left|2x\right|$ $x\ne 0$
$\log \left|x\right|$ is defined for $|x|>0$
$f\left(x\right)=\log 2x=\log 2+\log x$
$f^{\prime }\left(x\right)=0+\frac{1}{x}=\frac{1}{x}$