Question

If$f\left(x\right)=x|x|,then{f}^{\prime }(-2)=.....$

Answer 1

Given:

$f\left(x\right)=x|x|$

$Whenx<0$

$\Rightarrow f\left(x\right)=x(-x)=-x^2$

$\Rightarrow f^{\prime }\left(x\right)=-2x$

$\therefore f^{\prime }(-2)=4$