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

  • question_answer
    \[\frac{d}{dx}\{{{e}^{-a{{x}^{2}}}}\log (\sin x)\}=\]                                            [AI CBSE 1984]

    A)            \[{{e}^{-a{{x}^{2}}}}(\cot x+2ax\log \sin x)\]

    B)            \[{{e}^{-a{{x}^{2}}}}(\cot x+ax\log \sin x)\]

    C)            \[{{e}^{-a{{x}^{2}}}}(\cot x-2ax\log \sin x)\]

    D)            None of these

    Correct Answer: C

    Solution :

               \[\frac{d}{dx}\{{{e}^{-a{{x}^{2}}}}\log (\sin x)\}\]                    \[={{e}^{-a{{x}^{2}}}}(-2ax).\log (\sin x)+{{e}^{-a{{x}^{2}}}}\cot x\]                    \[={{e}^{-ax}}^{2}[\cot x-2ax\log (\sin x)]\].


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