The derivative of f(x) = x|x| is - Vidyadip

MCQ

The derivative of $f(x) = x|x|$ is

A
$2x$
B
$-2x$
C
$2{x^2}$
✓
$2|x|$

✓

Answer

Correct option: D.

$2|x|$

d
(d) $f(x) = \left\{ \begin{array}{l}- {x^2},\;x < 0\\{x^2}\;\;,\;\,\,x > 0\end{array} \right. $

$\Rightarrow f'(x) = \left\{ \begin{array}{l} - 2x\,,\,\,x < 0\\2x\,\,\,,\,\,\,\,x > 0\end{array} \right.\,\,\,$

$\therefore f'(x) = 2|x|$.

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