If $f(x) = |\cos x - \sin x|$, then $f'\left(\frac{\pi}{6}\right)$ is equal to?
$-\frac{1}{2}(1+\sqrt{3})$
$\frac{1}{2}(1+\sqrt{3})$
$-\frac{1}{2}(1-\sqrt{3})$
$\frac{1}{2}(1-\sqrt{3})$
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