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

  • question_answer
    If \[{{x}^{y}}={{e}^{x-y}}\], then \[\frac{dy}{dx}=\]             [MP PET 1987, 2004; MNR 1984; Roorkee 1954; BIT Ranchi 1991; RPET 2000]

    A)            \[\log x.{{[\log (ex)]}^{-2}}\]

    B)            \[\log x.{{[\log (ex)]}^{2}}\]

    C)            \[\log x.{{(\log x)}^{2}}\]

    D)            None of these

    Correct Answer: A

    Solution :

               \[{{x}^{y}}={{e}^{x-y}}\] Þ \[y\log x=x-y\] Þ \[y=\frac{x}{1+\log x}\]            Þ  \[\frac{dy}{dx}=\log x{{(1+\log x)}^{-2}}=\log x{{[\log ex]}^{-2}}\].


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