I'm having trouble with this problem. Please help =)

Lim

X-> Infinity Ln(lnx) / x

I know if you plug infinity in there it'll be infinity over infinity and that's when you apply the L'H rule. But when I take the derivative for that it comes out to

X * 1/lnx * 1/x - Ln(lnX)

------------------------

X^2

which would equal -infinity / infinity right? But that's not the answer. The answer is 0 but i'm having trouble getting to it. any help will be appreciated. Thanks.