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 \( a + b \).
by
Hobart Pao