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STD 12 - 5. continuity and differentiation — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 5. continuity and differentiation4 Marks
MCQ
The derivative of $f(x) = x|x|$ is
  • A
    $2x$
  • B
    $-2x$
  • C
    $2{x^2}$
  • D
    $2|x|$
✓

Answer

$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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