JEE Math Practice Question

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

1. A.$$g$$ is not differentiable at $$x=0$$
2. B.$$g'\left( 0 \right) = \cos \left( {\log 2} \right)$$
3. C.$$g'\left( 0 \right) = - \cos \left( {\log 2} \right)$$
4. D.$$g$$ is differentiable at $$x=0$$ and $$g'\left( 0 \right) = - \sin \left( {\log 2} \right)$$