I'm going to do something which somehow we are told never, ever to do,

我接下来要做一件以前绝对不允许的事情
which is to just cancel the dts.

约去这些dt
You all know that when you do dy/dx,

你们都知道当你算dy/dx时
you're not supposed to cancel that d.

你不能把d约掉
That's actually correct.

但这里其实是没问题的
You don't want to cancel the d in the derivative.

你不能在求导的时候约掉d
But this happens to be completely legitimate,

但这里所说的情况是完全合理的
so I'm going to assume it's true

所以我先假设这是对的
and I'll maybe take a second explaination why it's legitimate.

待会儿再进一步解释为什么合理
What this really means is in a given time,

这里的真正含义是在给定的一段时间内
the change in this quantity is

这个量的变化量等于
a times the change in this quantity.

a乘以这个量的变化量