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For x ∈ R, f(x) = |log 2 − sinx| and g(x) = f(f(x)), then:

1. g is not differentiable at x = 0
2. g'(0) = cos(log 2)
3. g'(0) = − cos(log(2))
4. g is differentiable at x = 0 and g'(0) = − sin(log2)

Correct answer: g'(0) = cos(log 2)

Solution

The correct option states that g'(0) = cos(log 2) because the composition of functions preserves differentiability, and at x = 0, the derivative of f(x) evaluated at that point leads to this result based on the chain rule.

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