Question

If $f\left(x\right)=\frac{x^2}{|x|}$, write $\frac{d}{dx}\left(f\right(x\left)\right).$

Answer 1

We have,

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

$=\{\begin{array}{c}1[ifx>0]\\ -1,[ifx<0]\end{array}$