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JEE Main & Advanced Mathematics Differentiation Question Bank Differentiation of implicit function Parametric

  • question_answer
    If \[y=\log {{x}^{x}},\]then \[\frac{dy}{dx}=\]                                                          [MNR 1978]

    A)            \[{{x}^{x}}(1+\log x)\]

    B)            \[\log (ex)\]

    C)            \[\log \left( \frac{e}{x} \right)\]

    D)            None of these

    Correct Answer: B

    Solution :

               \[y=\log {{x}^{x}}=x\log x\]            Differentiating w.r.t. x, we get                    \[\frac{dy}{dx}=(1+\log x)=\log e+\log x=\log (ex)\]  \[(\because \log e=1)\].


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