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

Answer 1

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))