Question

If $f\left(x\right)=|x|$ the $f^{\prime }\left(x\right)$, where $x\ne 0$ is equal to

• A. $-2$
• B. $0$
• C. $-1$
• D. $\frac{|x|}{x}$

Answer 1

The correct option is D $\frac{|x|}{x}$

$f\left(x\right)=|x|=\{\begin{array}{cc}-x& x\le 0\\ x& x>0\end{array}$

$f^{\prime }\left(x\right)=\{\begin{array}{cc}-1& x<0\\ 1& x>0\end{array}$

$f^{\prime }\left(x\right)=\frac{|x|}{x}=\{\begin{array}{cc}-1& x<0\\ 1& x>0\end{array}$

Hence, option D is correct.