Let `y=sqrt(x+sqrt(x+sqrt(x+...oo)))," then "(dy)/(dx)` is equal to

Options

A. `(1)/(2y-1)`
B. `(x)/(x+2y)`
C. `(1)/(sqrt(1+4x))`
D. `(y)/(2x+y)`

Explanation

To solve the problem where \( y = \sqrt{x + \sqrt{x + \sqrt{x + \ldots}}} \), we will follow these steps:

### Step 1: Set up the equation
We start by recognizing that the expression inside the square root continues infinitely. Therefore, we can set up the equation:
\[ y = \sqrt{x + y} \]

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