# Write the Value of D D X { ( X + | X | ) | X | } - Mathematics

Write the value of $\frac{d}{dx} \left\{ \left( x + \left| x \right| \right) \left| x \right| \right\}$

#### Solution

$\text{ Case } 1:$
$x > 0$
$\left| x \right| = x$
$\left( x + \left| x \right| \right)\left| x \right|$
$= \left( x + x \right)x$
$= 2 x^2$
$\frac{d}{dx}\left[ \left( x + \left| x \right| \right)\left| x \right| \right] = \frac{d}{dx}\left( 2 x^2 \right) = 4x \left( 1 \right)$
$\text{ Case } 2:$
$x < 0$
$\left| x \right| = - x$
$\left( x + \left| x \right| \right)\left| x \right|$
$= \left( x - x \right)x$
$= 0$
$\frac{d}{dx}\left[ \left( x + \left| x \right| \right)\left| x \right| \right] = \frac{d}{dx}\left( 0 \right) = 0 \left( 2 \right)$
$\text{ From } (1) \text{and} (2), \text{ we have}:$
$\frac{d}{dx}\left[ \left( x + \left| x \right| \right)\left| x \right| \right] = \binom{4x, if x > 0}{0, if x < 0}$


Concept: The Concept of Derivative - Algebra of Derivative of Functions
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Q 6 | Page 47