PROFESSOR: All right. As you're settling in, why don't you take 10 more seconds to answer the clicker question.

教授：好，既然你们都坐好了,给你们10秒钟回答这个问题。

麻省理工公开课 - 化学原理课程节选

The basic idea in solving these equations and integrating is you find one answer, so then when you take enough derivatives, the function does what it's supposed to do.

解决这类方程以及积分的基本思想就是,你求出一个解,然后进行多次求导,求导的结果就满足条件

耶鲁公开课 - 基础物理课程节选

Well, unfortunately, we know this is not the right answer, because if you take the first derivative, I get 2t.

遗憾的是,我们知道这还不是正确答案,因为如果对它求一阶导数,会得到2t

耶鲁公开课 - 基础物理课程节选

If you want to know how fast it's moving at a given time, if you want to know the velocity, I just take the derivative of this answer, which is 10-10t.

如果你想知道它在给定时刻的运动有多快,如果你想知道它的速度,我只要对这个式子求导,得到10-10t

耶鲁公开课 - 基础物理课程节选