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If f (x) = log(x) (log x), then f'(x) a...

If ` f (x) = log_(x) (log x)`, then f'(x) at x = e is …….. .

Text Solution

Verified by Experts

The correct Answer is:
`1/e`
Given, `" "f(x) = log_(x) (log x) `
`:." " f(x) = (log (log x))/(log x) `
On differentiating both sides, we get
`f'(x)=((log x)(1/(log x)*1/x)-log (log x)*1/x)/((log x)^(2)) `
`:." " f'(e)=(1*(1/1*1/e)-log(1)*1/e)/((1)^(2))`
` rArr f'(e) = 1/e`
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