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Question:

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

1. $\mathrm{g}$ is differentiable at $\mathrm{x}=0$ and $\mathrm{g}^{\prime}(0)=-\sin (\log 2)$

2. $\mathrm{g}$ is not differentiable at $\mathrm{x}=0$

3. $\mathrm{g}^{\prime}(0)=\cos (\log 2)$

4. $g^{\prime}(0)=-\cos (\log 2)$

Correct Option: , 3

Solution: