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If F (X) = X 2 | X | , Write D D X ( F ( X ) ) - Mathematics

If f (x) = \[\frac{x^2}{\left| x \right|},\text{ write }\frac{d}{dx}\left( f (x) \right)\] 

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Solution

\[\text{ Case } 1: x>0\]
\[\left| x \right| = x\]
\[f\left( x \right) = \frac{x^2}{\left| x \right|} = \frac{x^2}{x} = x\]
\[f'\left( x \right) = 1\]
\[\text{ Case } 2: x<0\]
\[\left| x \right| = - x\]
\[f\left( x \right) = \frac{x^2}{\left| x \right|} = \frac{x^2}{- x} = - x\]
\[f'\left( x \right) = - 1\]
\[\text{ From case 1 and case 2, we have }:\]
`f'(x)={(1, if, x > 0),(-1, if, x < 0):}`

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Q 9 | Page 47
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