For x∈R,f(x)=log2−sinx and g(x)=f(f...
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For ( x in mathbf{R}, f(x)=log 2-sin x ) and ( g(x)=f(f(x)) ), then
(a) ( g ) is not differentiable at ( x=0 )
(b) ( g^{prime}(0)=cos (log 2) )
(c) ( g^{prime}(0)=-cos (log 2) )
(d) ( g ) is differentiable at ( x=0 ) and ( g^{prime}(0)=-sin (log 2) )

JEE/Engineering Exams
Maths
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For x∈R,f(x)=log2−sinx and g(x)=f(f(x)), then
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( f(x)=log 2-sin x mid, x in mathbf{R} )
Let ( a=sin ^{-1}(log 2) )
For ( -a Rightarrow g(x)=f(f(x))=log 2-sin (f(x)) )
( =log 2-sin (log 2-sin x) )
( Rightarrow g^{prime}(x)=(-cos (log 2-sin x))(-cos x) )
( therefore g^{prime}(0)=(-cos (log 2))(-1)=cos (log 2) )

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