Question

For x∈R, f(x) = |log2 – sinx| and g(x) = f(f(x)), then:

(1) g is differentiable at x = 0 and g'(0) = –sin(log2)

(2) g is not differentiable at x = 0

(3) g'(0) = cos(log2)

(4) g'(0) = –cos(log2)

Answer with reason....
And Nhi aata toh Chup baitho -,-​

Answer 1

Here is ur Answer :

g(x) = f(f(x))

g'(x) = f'(f(x)) f'(x)

g'(0) = f'(f(0)) f'(0)

x ➝ 0 log2 > sinx

f(x) = - sinx

f'(x) = 0 - cosx

f'(log2) = -cos(log2)

g'(0) = (-cos(log2)). (-1)

$\small{ \red{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies{ \sf{g'(0) = \cos( log2)}}}}$