\[y=\sqrt { x+\sqrt { x+\sqrt { x+\sqrt { x+\cdots }}}}\]

For \( x>0 \) , define \(y\) as above. What is \(\dfrac{dy}{dx}\)?

- \(P: \dfrac{1}{2y-1}\)
- \(Q: \dfrac{x}{x+2y}\)
- \(R: \dfrac { 1 }{ \sqrt { 1+4x } } \)
- \(S: \dfrac{y}{2x + y}\)

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