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

  • question_answer
    If \[f(x)=({{\log }_{\cot x}}\tan x){{({{\log }_{\tan x}}\cot x)}^{-1}},\]then \[f'(2)=\]

    A)            2

    B)            0

    C)            \[\frac{1}{2}\]

    D)            ? 2

    Correct Answer: B

    Solution :

               Obviously, \[f(x)={{({{\log }_{\cot x}}\tan x)}^{2}}\]                                                                                                                       \[={{({{\log }_{\cot x}}{{(\cot x)}^{-1}})}^{2}}\Rightarrow f'(x)=0\] .


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