MCQ
${d \over {dx}}\sqrt {x\sin x} = $
  • ${{\sin x + x\cos x} \over {2\sqrt {x\sin x} }}$
  • B
    ${{\sin x + x\cos x} \over {\sqrt {x\sin x} }}$
  • C
    ${{x\sin x + \cos x} \over {\sqrt {2\sin x} }}$
  • D
    ${{\sin x + x\cos x} \over {\sqrt {2x\sin x} }}$

Answer

Correct option: A.
${{\sin x + x\cos x} \over {2\sqrt {x\sin x} }}$
a
(a) Let ${y^2} = x\sin x \Rightarrow 2y\frac{{dy}}{{dx}} = \sin x + x\cos x$

$\therefore \frac{{dy}}{{dx}} = \frac{{[\sin x + x\cos x]}}{{2\sqrt {x\sin x} }}$.

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