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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)`

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To solve the problem, we start with the given equation: \[ y = \sqrt{x + \sqrt{x + \sqrt{x + \ldots}}} \] ### Step 1: Rewrite the equation Since the expression inside the square root is the same as \( y \), we can rewrite the equation as: \[ y = \sqrt{x + y} \] ...
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