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If f(x)=cos^(-1)[(1-(logx)^2)/(1+(logx)^...

If `f(x)=cos^(-1)[(1-(logx)^2)/(1+(logx)^2)]` , then the value of `f'(e)` is equal to........

A

`1/e`

B

`2/(e^(2))`

C

`2/e`

D

1

Text Solution

Verified by Experts

The correct Answer is:
A
We have
`f(x)=cos^(-1)[(1-(logx)^(2))/(1+(logx)^(2))]`
`f(x)=2tan^(-1)(logx)[becausecos^(-1)((1-x^(2))/(1+x^(2)))=2tan^(-1)x]`
`f'(x)=2/(1+(logx)^(2))xx1/x`
`f'(e)=2/(1+1)xx1/e=1/e`
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