$f$“主导”(“被……主导”)$g$

Intuitively, we understand what domination means. What does it mean in calculus?

Domination is a highly informal term relating two functions. We say that one function dominates another if the magnitude of the ratio of the first function to the second increases without bound as the input increases without bound.

More concisely, $f(x)$ dominates $g(x)$ if $\lim_{x\to \infty}\frac{g(x)}{f(x)}=0$.

There is no common notation for this idea, but the notation $\ll$ ("much less than") or $\gg$ ("much greater than") is sometimes used.

Here is an example: $$a^x \gg x^p \gg x^q \gg \log_b{x}$$ The above holds if $a,b>1$ and $p>q$.

By L'Hospital's Rule, $f(x)$ dominates $g(x)$ if and only if $f'(x)$ dominates $g'(x)$.