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

  • question_answer
    \[\frac{d}{dx}{{\log }_{\sqrt{x}}}(1/x)\]is equal to                                                         [AMU 1999]

    A)            \[-\frac{1}{2\sqrt{x}}\]

    B)            ? 2

    C)            \[-\frac{1}{{{x}^{2}}\sqrt{x}}\]

    D)            0

    Correct Answer: D

    Solution :

               \[f(x)={{\log }_{\sqrt{x}}}\left( \frac{1}{x} \right)=\frac{\log \left( \frac{1}{x} \right)}{\log \sqrt{x}}=\frac{(-1)\log x}{(1/2)\,\log x}=-2\]                    Þ \[{f}'(x)=0\].


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