If y=sqrt(x+sqrt(x+sqrt(x+...tooo))), pr...

If `y=sqrt(x+sqrt(x+sqrt(x+...tooo))),` prove that `(dy)/(dx)=1/(2y-1)`

AI Generated Solution

To solve the problem, we need to prove that if \[ y = \sqrt{x + \sqrt{x + \sqrt{x + \ldots}}} \] then \[ \frac{dy}{dx} = \frac{1}{2y - 1}. \] ...

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