If \[y=\sqrt{x+\sqrt{x+\sqrt{x+........\text{to}}}}\infty \,,\,\text{then}\frac{dy}{dx}=\] [RPET 2002]

• A. \[\frac{x}{2y-1}\]
• B. \[\frac{2}{2y-1}\]
• C. \[\frac{-1}{2y-1}\]
• D. \[\frac{1}{2y-1}\]