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JEE Main & Advanced Mathematics Differentiation Question Bank Mock Test - Limits and Derivatives

  • question_answer
    If \[y=\sqrt{\log x+\sqrt{\log x+\sqrt{\log x+...\infty },}}\]then \[\frac{dy}{dx}\]is

    A) \[\frac{x}{2y-1}\]         

    B) \[\frac{x}{2y+1}\]

    C) \[\frac{1}{x(2y-1)}\]     

    D) \[\frac{1}{x(1-2y)}\]

    Correct Answer: C

    Solution :

    [c] \[y=\sqrt{\operatorname{logx}+y}\] Or \[{{y}^{2}}=\log x+y\] Or \[2y\frac{dy}{dx}=\frac{1}{x}+\frac{dy}{dx}\] or \[\frac{dy}{dx}=\frac{1}{x(2y-1)}\]


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