a) Show that the function f(x)=x^x is increasing on [e^-1,\infty)

Done this bit

b) If g is the inverse function f restricted to [e^-1,\infty) show that

\lim_{x \to \infty} (g(y)ln(ln(y)))/(ln(y))=1

Hint: Start with the equation y = x^x and take ln of both sides twice

Just stuck on section b of this question, any help would be great.