In the neighborhood of x=0,f(x)=log2−sinx
∴ g(x)=f(f(x))=log2−sin(f(x))
=log2−sin(log2−sinx)
∴ g′(x)=−cos(log2−sinx)(–cosx)
∴ g′(0)=cos(log2)
For x∈R,f(x)=∣log2−sinx∣ and g(x)=f(f(x)), then
Held on 3 Apr 2016 · Verified 6 Jul 2026.
g′(0)=−cos(log2)
g is differentiable at x=0 and g′(0)=−sin(log2)
g is not differentiable at x=0
g′(0)=cos(log2)
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