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If Y = X | X | , Find D Y D X for X < 0 ? - Mathematics

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Question

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

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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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Chapter 11: Differentiation - Exercise 11.09 [Page 118]

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RD Sharma Mathematics [English] Class 12
Chapter 11 Differentiation
Exercise 11.09 | Q 12 | Page 118

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