For `x in R, f(x) =|log_(e) 2-sinx| and g(x) = f(f(x)) ,` then

Options

A. g is not differerentiable at x=0
B. g'(0)=cos(log2)
C. g'(0)=-cos(log 2)
D. g is differentiable at x=0 and g'(0)=-sin (log 2)

Answer

B

Explanation

We have `,f(x)=|log 2-sinx|`
`therefore g(x)=f(f(x))=|log 2-sin|log 2-sinx||`
In the neighborhood of x=0, we have
`g(x)=log 2-sin (log 2-sin x)`
Which is continuous and differentiable. So, g(x) is differentiable at x=0 and g'(x)=+cos(log 2-sinx) cos x.
`therefore g'(0)=cos(log2)`