Question

If f(x) = |x|, then f’(x), where $x\ne 0$ is equal to

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

Answer 1

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

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