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MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

For x∈Rx \in R , f(x)=log⁡2−sin⁡xf(x) = \log 2 - \sin x and g(x)=f(f(x))g(x) = f(f(x)) , then (1) gg is not differentiable at x=0x = 0 (2) g′′(0)=cos⁡(log⁡2)g''(0) = \cos(\log 2) (3) g′′(0)=−cos⁡(log⁡2)g''(0) = -\cos(\log 2) (4) gg is differentiable at x=0x = 0 and g′′(0)=−sin⁡(log⁡2)g''(0) = -\sin(\log 2)

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