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Calculus

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If y=Root of(logx+root of (logx+root of logx.........infinty)...prove that dy/dx=1/x(2y-1)

  • Calculus - ,

    y = √(lnx+√(lnx+√(lnx+...)))
    y^2 = lnx+√(lnx+√(lnx+...))) = lnx + y

    2y y' = 1/x + y'
    (2y-1)y' = 1/x
    y' = 1/(x(2y-1))

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