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Let $f(x)=\cos(g(x))$, where values for $g(x)$ and $g'(x)$ are given in the table below.

$$x \hspace{1.5cm}$$ 0 1 2
$g(x)$ $\cfrac{\pi}{3}$ $\cfrac{\pi}{4}$ $\cfrac{\pi}{6}$
$g'(x)$ 1 2 3



Find $f'(1)$.

A

$-\sqrt{2}$

B

$\cfrac{-\sqrt{2}}{2}$

C

$\cfrac{\sqrt{2}}{2}$

D

$\sqrt{2}$

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