Question

If f(x) =log_x (log x), then f'(x) at x = e is ______.

Options

• e

• `1/e`

• 1

• None of these

Answer 1

If f(x) =log_x (log x), then f'(x) at x = e is `underline(1/e)`.

Explanation:

f(x) =log_x (log x) `=(log(log x))/(log x)`

`thereforef^'(x)=(logx*1/logx*d/dx(log x)-log(log x)*1/x)/(log x)^2`

`=(1/x-1/x log(logx))/(log x)^2`

`thereforef^'(e)=(1/e-0)/1^2=1/e`