Nested radical differentiation

Calculus Level 3

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

If \( \left. \dfrac{dy}{dx} \right|_{x=3} \) can be represented in the form \( \dfrac{a}{b} \), where \(a, b\) are coprime positive integers, find \( a + b \).

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