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

  • question_answer
     If \[{{x}^{y}}.{{y}^{x}}=1\], then \[\frac{dy}{dx}\]=

    A)            \[\frac{y\,(y+x\log y)}{x(y\log x+x)}\]

    B)            \[\frac{y\,(x+y\log x)}{x(y+x\log y)}\]

    C)            \[-\frac{y(y+x\log y)}{x(x+y\log x)}\]

    D)            None of these

    Correct Answer: C

    Solution :

               \[y\log x+x\log y=0\]; \[\therefore \]\[\frac{dy}{dx}=\frac{\partial f/\partial x}{\partial f/\partial y}\].


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