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Question
If \[y = x \left| x \right|\] , find \[\frac{dy}{dx} \text{ for } x < 0\] ?
Solution
\[\text{ We have, y } = x\left| x \right|\]
\[ \Rightarrow y = x\left( - x \right) \left( \because x < 0 \right)\]
\[ \Rightarrow y = - x^2\]
\[\Rightarrow \frac{dy}{dx} = \frac{d}{dx}\left( - x^2 \right)\]
\[ \Rightarrow \frac{dy}{dx} = - 2x\]
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