Crazy Calculus 7

Calculus Level 3

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

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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