If $\displaystyle f(x)=ln(ln\:x)$, find the value of $\displaystyle f'(\frac{1}{e})$

Choices:

a)$\displaystyle -\frac{1}{e}$

b)undefined

c)$\displaystyle \frac{1}{e}$

d)$\displaystyle 2e$

e)$\displaystyle \sqrt{e}$

alright, heres where im at right now:

1)It could be undefined because $\displaystyle \frac{1}{e}$ is not in the domain of f(x)?

2)the answer is $\displaystyle -e$ and my prof made a mistake(seems unlikely since he's been doing this for 20 years)?

3)my friend says its $\displaystyle \frac{1}{e}$?

Can anyone confirm which is correct with justification?

Thanks!