For $x \in \mathbb{R}$, $f(x) = |\log 2 - \sin x|$ and $g(x) = f(f(x))$, then: (1) $g'(0) = \cos(\log 2)$ (2) $g'(0) = -\cos(\log 2)$ (3) $g$ is differentiable at $x=0$ and $g'(0) = -\sin(\log 2)$ (4) $g$ is not differentiable at $x=0$