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

  • question_answer
    If \[y=\log \log x\], then \[{{e}^{y}}\frac{dy}{dx}=\]                                    [MP PET 1994, 95]

    A)            \[\frac{1}{x\log x}\]

    B)            \[\frac{1}{x}\]

    C)            \[\frac{1}{\log x}\]

    D)            \[{{e}^{y}}\]

    Correct Answer: B

    Solution :

               \[y={{\log }_{e}}{{\log }_{e}}x\Rightarrow {{e}^{y}}={{\log }_{e}}x\Rightarrow {{e}^{y}}\frac{dy}{dx}=\frac{1}{x}\].


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