.I'm supposed to use l'Hopital's rule to calculate:

lim x-->infinity: [ln(ln(x))]/[xln(x)]

I know I find the derivative of the numerator and the derivative of the denominator.

For the numerator: Dx ln(ln(x)) = 1/(ln(x))

For the denominator (product rule since I have two terms, x, and ln(x) ) Dx xln(x) = (ln(x)) (x(1/x))

I'm not sure if that's correct or not, but I know I have to actually calculate the limit and that doesn't seem possible with the way the equations stands after the first derivative of the numerator and denominator. If somebody could show me what I have to do next that would be great.

Thanks