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If f(x)=cos^(-1){(1-(log(e)x)^(2))/(1+(l...

If `f(x)=cos^(-1){(1-(log_(e)x)^(2))/(1+(log_(e)x)^(2))},` then `f'((1)/( e ))` is equal to

A

e

B

`-e`

C

1

D

`2e`

Text Solution

Verified by Experts

The correct Answer is:
B
In the neighbourhood of `x=(1)/( e ),` we find that `log_(e)xlt0.`
`:." "f(x)=cos^(-1){(1-(log_(e)x)^(2))/(1+(log_(e)x)^(2))}=-2tan^(-1)(log_(e)x)`
`implies" "f'(x)=(2)/(1+(log_(e)x)^(2))xx(1)/(x)impliesf'((1)/(e))=-e.`
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