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

  • question_answer
    \[\frac{d}{dx}{{e}^{x\sin x}}=\]                          [DSSE 1979]

    A)            \[{{e}^{x\sin x}}(x\cos x+\sin x)\]

    B)            \[{{e}^{x\sin x}}(\cos x+x\sin x)\]

    C)            \[{{e}^{x\sin x}}(\cos x+\sin x)\]

    D)            None of these

    Correct Answer: A

    Solution :

               Let\[y={{e}^{x\sin x}}\]Þ \[\log y=x\sin x\]                    \[\therefore \frac{1}{y}\frac{dy}{dx}=\sin x+x\cos x\]or \[\frac{dy}{dx}={{e}^{x\sin x}}(\sin x+x\cos x)\].


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