It's constant pressure. OK, so now, last time you looked at the Joule expansion to teach you how to relate derivatives like du/dV.

这是恒压的，好，上节课你们,学习了焦耳定律,以及怎样进行导数间的变换。

麻省理工公开课 - 热力学与动力学课程节选

If I gave you the location of a particle as a function of time, you can find the velocity by taking derivatives.

如果我给出物体的位移是时间的函数,你可以通过求导来得到速度

耶鲁公开课 - 基础物理课程节选

We can start taking derivatives of this with respect to time.

我们首先来对时间求微分

耶鲁公开课 - 基础物理课程节选

You can actually take derivatives of a vector with time.

你可以直接求位矢对时间的导数

耶鲁公开课 - 基础物理课程节选

The most important result from last time was that if you took this r, and you took two derivatives of this to find the acceleration, d^2 r over dt^2, try to do this in your head.

上节课最重要的结论,就是如果你把 r 写成这样,对 r 求两次导就能得到加速度,d^2 r / dt^2,心算一下

耶鲁公开课 - 基础物理课程节选

if I say a particle's location is i times t^2 plus j times 9t^3, for every value of time, you can put the numbers in and you can find the velocity by just taking derivatives.

一个质点的位置,i ? t^2 + j ? 9t^3,在每一个时间点,你可以把数值代入,并通过求导得到速度

耶鲁公开课 - 基础物理课程节选