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JEE Main 2016

JEE Main 2016 Mathematics question on Limits Continuity and Differentiability

For x∈Rx \in R, f(x)=∣log⁡2−sin⁡x∣f(x) = |\log 2 - \sin x| and g(x)=f(f(x))g(x) = f(f(x)), then
  1. A.
    g is not differentiable at x=0x = 0
  2. B.
    g′(0)=cos⁡(log⁡2)g'(0) = \cos(\log 2)
  3. C.
    g′(0)=−cos⁡(log⁡2)g'(0) = -\cos(\log 2)
  4. D.
    g is differentiable at x=0x = 0 and g′(0)=−sin⁡(log⁡2)g'(0) = -\sin(\log 2)
Show answer

Correct option: B

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