Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

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

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

#### 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):}

Concept: The Concept of Derivative - Algebra of Derivative of Functions
Is there an error in this question or solution?

#### APPEARS IN

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