Nested radical differentiation

Calculus Level 3

y=x+xx+xx+ y = \sqrt{x+\sqrt{x-\sqrt{x+\sqrt{x-\sqrt{x+\cdots}}}}}

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

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