Exercise 2, § 3

Let $f$ and $g$ be two functions $\geqslant 0$ tending to $+\infty$ with $x$ and comparable to order 1; $h$ is a differentiable function, $\geqslant 0$ and increasing as $x$ tends to $+\infty$, show that $hf$ and $hg$ are comparable to order 1.