Consider the function
\[ f(x) = \sqrt{x+\sqrt{x+\sqrt{x+\cdots}}}. \]
If the gradient of the tangent of the function at \( x = 12 \) can be expressed as \( \frac{a}{b},\) where \( a \) and \( b \) are coprime positive integers, what is the value of \( a + b?\).
by
Cole Coupland
