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

  • question_answer
    If\[y={{\log }_{\sin x}}(\tan x),\] then \[{{\left( \frac{dy}{dx} \right)}_{\pi /4}}=\]

    A)            \[\frac{4}{\log 2}\]

    B)            \[-4\log 2\]

    C)            \[\frac{-4}{\log 2}\]

    D)            None of these

    Correct Answer: C

    Solution :

               \[y=\frac{\log \tan x}{\log \sin x}\]                    Þ  \[\frac{dy}{dx}=\frac{(\log \sin x)\left( \frac{{{\sec }^{2}}x}{\tan x} \right)-(\log \tan x)(\cot x)}{{{(\log \sin x)}^{2}}}\]                    Þ  \[{{\left( \frac{dy}{dx} \right)}_{\pi /4}}=\frac{-4}{\log 2}\]       (On simplification).


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