L’Hôpital’s rule practice question 4

As $x \to \infty$, what do $\log x$ and $\sqrt{x}$ each do? Name the form before choosing how to compare them.

Top and bottom both grow without bound, so the form is $\tfrac{\infty}{\infty}$. Differentiate each: $\tfrac{1}{x}$ and $\tfrac{1}{2\sqrt{x}}$.