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If f(x)=log(e)(log(e)x)/log(e)x then f'(...

If `f(x)=log_(e)(log_(e)x)/log_(e)x` then `f'(x)` at x = e is

A

0

B

1

C

e

D

`1//2`

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)=(log_(e)(log_(e)x))/(log_(e)x)`
`therefore" "f'(x)=((1)/(log_(e)x)xx(1)/(x)xxlog_(e)(x)-log_(e)(log_(e)(x))xx(1)/(x))/([log_(e)(x)]^(2))`
`therefore" "f'(e)=((1)/(e)-0)/(1)=1//e`
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