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let f(x)=x^(3)l n(x^(2)(g(x)), where g(x...

let `f(x)=x^(3)l n(x^(2)(g(x))`, where `g(x)` is a differentiable positive function on `(0,infty)` satisfying `g(2)=(1)/(4),g^(')(2)=-3`, then `f'^(2)` is

A

77

B

88

C

`-88`

D

`-77`

Text Solution

Verified by Experts

The correct Answer is:
C
`becausef'(x)=x^(3).(1)/(x^(2)g(x)).{2xg{x}+x^(2)g^(')(x)}+3x^(2)l n (x^(2)g(x))`
`thereforef'(2)=(8)/(4xxg(2)){4g(2)+4g^(')(2)}+3xx4l n(4g(2))`
`f'(2)=-88`
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