Nested Squareroot

Calculus Level 2

Consider the function

\( f(x) = \sqrt{x+\sqrt{x+\sqrt{x+\ldots}}} \)

If the gradient of the tangent of the function at \( x = 12 \) can be expressed as \( \frac{a}{b} \) where \( a \) and \( b \) are positive coprime integers, what is the value of \( a + b \).

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