Question

Write the value of $\frac{d}{dx}\left(x|x|\right).$

Answer 1

We have,

$\frac{d}{dx}x|x|=\{\begin{array}{c}\frac{d}{dx}{x}^2[ifx>0]\\ \\ \frac{d}{dx}(-x)x[ifx<0]\end{array}$

$=\{\begin{array}{c}2x[ifx>0]\\ -2x[ifx<0]\end{array}$