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Let f : (-5,5)rarrR be a differentiable ...

Let `f : (-5,5)rarrR` be a differentiable function of with `f(4) = 1, f'(4)=1, f(0) = -1 and f'(0) =1 If, g(x)=(f(2f^(2)(x)+2))^(2),` then g'(0) equals

A

-2

B

4

C

-4

D

0

Text Solution

Verified by Experts

`g'(x)=2[f(2f(x)+2)][(d)/(dx)(f(2f(x)+2))]`
`=2[f(2f(x)+2)][f'(2+f(x)+2)xx2f'(x)]`
`rArr" "g'(0)=2f(2f(0)+2)f'(2f(0)+2)2f'(0)`
`=4f(0)[f'(0)]^(2)`
`4(-1)(1)=-4`
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