For $x \in R, \; f(x) = | \log 2 - \sin x |$ and $g(x) = f( f(x))$, then :

Question

( A ) $g$ is not differentiable at $x=0$
( B ) $g'(0) = \cos (\log 2)$
( C ) $g'(0) =- \cos (\log 2)$
( D ) $g$ is differentiable at $x=0$ and $g'(0) = -\sin (\log 2)$