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

  • question_answer
    If \[{{x}^{2}}+{{y}^{2}}=t-\frac{1}{t},\]\[{{x}^{4}}+{{y}^{4}}={{t}^{2}}+\frac{1}{{{t}^{2}}}\], then \[{{x}^{3}}y\frac{dy}{dx}=\]

    A)            1

    B)            2

    C)            3

    D)            4

    Correct Answer: A

    Solution :

               \[{{x}^{4}}+{{y}^{4}}={{\left( t-\frac{1}{t} \right)}^{2}}+2={{({{x}^{2}}+{{y}^{2}})}^{2}}+2\]                    Þ  \[{{x}^{2}}{{y}^{2}}=-1\Rightarrow {{y}^{2}}=-\frac{1}{{{x}^{2}}}\]                    Differentiating, we get \[2y\frac{dy}{dx}=\frac{2}{{{x}^{3}}}\]or\[{{x}^{3}}y\frac{dy}{dx}=1\].


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