\textbf{119.} If $f$ is a differentiable function, $g(x) = f\!\left(\sqrt{1 + \tan^2 x}\right)$, and $g'\!\left(\dfrac{\pi}{3}\right) = \dfrac{\sqrt{3}}{2}$, what is the value of $f'(2)$?
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(1) $-\dfrac{1}{2}$ \hfill (2) $\dfrac{1}{4}$ \hfill (3) $\dfrac{1}{2}$ \hfill (4) $1$
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