Question

If \[y = x \left| x \right|\] , find \[\frac{dy}{dx} \text{ for } x < 0\] ?

Answer 1

\[\text{ We have, y } = x\left| x \right|\]

\[ \Rightarrow y = x\left( - x \right) \left( \because x < 0 \right)\]

\[ \Rightarrow y = - x^2\] 

\[\Rightarrow \frac{dy}{dx} = \frac{d}{dx}\left( - x^2 \right)\]

\[ \Rightarrow \frac{dy}{dx} = - 2x\]