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

  • question_answer
    If \[x={{\sin }^{-1}}(3t-4{{t}^{3}})\] and \[y={{\cos }^{-1}}\,\,\sqrt{(1-{{t}^{2}})}\], then \[\frac{dy}{dx}\] is equal to                        [Kerala (Engg.) 2002]

    A)            ½

    B)            2/5

    C)            3/2

    D)            1/3

    Correct Answer: D

    Solution :

               \[y={{\cos }^{-1}}\sqrt{1-{{t}^{2}}}={{\sin }^{-1}}t\]            and \[\frac{du}{ds}=2x\,.\,\frac{dx}{ds}+2y\,.\,\frac{dy}{ds}\]                    \[\frac{{{d}^{2}}y}{d{{s}^{2}}}=0\] Þ \[y=2s-t\].


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