Let `y=sqrt(x+sqrt(x+sqrt(x+oo)))` , `(dy)/(dx)` is equal to `1/(2y-1)` (b) `x/(x+2y)` `1/(sqrt(1+4x)` (d) `y/(2x+y)`

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 need to find \( \frac{dy}{dx} \).

### Step-by-step Solution:

1. **Set up the equation**:
Since \( y \) is defined as \( y = \sqrt{x + \sqrt{x + \sqrt{x + \ldots}}} \), we can express this recursively. Therefore, we can write:
\[
y = \sqrt{x + y}
...