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if f(x)=(x^(3)-3x^(2)+3x-x^(2)l n(e^((1)...

if `f(x)=(x^(3)-3x^(2)+3x-x^(2)l n(e^((1)/(x^(2)))(x^(2)-x+2)))/(l n(x^(2)-x+2))`
then `f^('')(1)` is equal to

A

`(2)/((l n2)^(2))`

B

`-2`

C

`(-2)/((l n2)^(2))`

D

`(1-2l n2)/((l n2)^(4))`

Text Solution

Verified by Experts

The correct Answer is:
B
`f(x) (x^(3)-3x^(2)+3x-1-x^(2)l n (x^(2)-x+2))/(l n (x^(2)-x+2))`
`=((x-1)^(3))/(l n(x^92)-x+2)`
`thereforef^('')(1)=-2`
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