So, the fundamental theorem of calculus, not for line integrals, tells you if you integrate a derivative, then you get back the function.

微积分基本定理，不是曲线积分的，告诉我们，如果对函数的导数积分，就会得回原函数。

youdao

So, a function of several variables doesn't have the usual derivative.

因此，一个多变量的函数没有通常的导数。

youdao

It is the same thing as, in one variable calculus, when you take the anti-derivative of a function it is only defined up to adding the constant.

相当于在一元微积分中，取一个函数的不定积分，仅仅需要在结果后加一个常数。

youdao

If you knew only the third derivative of the function, you can have something quadratic in t without changing the outcome.

如果方程里有三阶导数,你就可以引入一个二次项,但是结果却不会变

耶鲁公开课 - 基础物理课程节选

Mathematically complete problem is that you can find the function x of t by saying that the second derivative of the function is equal to -k over m times the function.

这个数学问题就是,你可以求出函数 x,只要令函数的二阶导数,等于 -k 除以 m 再乘以函数

耶鲁公开课 - 基础物理课程节选

I tell you something about the second derivative of a function and ask you what is the function.

我告诉你一个函数的二阶导数,然后问你这个函数是什么

耶鲁公开课 - 基础物理课程节选