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JEE Main & Advanced Mathematics Differentiation Question Bank Derivative at a point Standard Differentiation

  • question_answer
    \[\frac{d}{dx}\sqrt{x\sin x}=\]                              [AISSE 1985]

    A)            \[\frac{\sin x+x\cos x}{2\sqrt{x\sin x}}\]

    B)            \[\frac{\sin x+x\cos x}{\sqrt{x\sin x}}\]

    C)            \[\frac{x\sin x+\cos x}{\sqrt{2\sin x}}\]

    D)            \[\frac{\sin x+x\cos x}{2\sqrt{x\sin x}}\]

    Correct Answer: A

    Solution :

               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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