\textbf{112-} The derivative of $f(x) = \sin\!\left(\dfrac{\pi}{2} + \tan^{-1}\dfrac{x}{2}\right)$ at the point $x = 2\sqrt{3}$ is which of the following?
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(1) $-\dfrac{1}{24}$ \hfill (2) $-\dfrac{1}{16}$ \hfill (3) $\dfrac{1}{8}$ \hfill (4) $\dfrac{1}{4}$
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