Question

If $y=x\left|x\right|$, find $\frac{dy}{dx}\mathrm{for}x<0$.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have},y=x\left|x\right| \\ \Rightarrow y=x\left(-x\right)\left(\because x<0\right) \\ \Rightarrow y=-x^2 \end{gathered}$$

$$\begin{gathered} \Rightarrow \frac{dy}{dx}=\frac{d}{dx}\left(-x^2\right) \\ \Rightarrow \frac{dy}{dx}=-2x \end{gathered}$$