Well, we already know what dA/dT at constant V is.

我们知道恒定体积下的。

麻省理工公开课 - 热力学与动力学课程节选

v We don't know what it is yet. In order to change this from a p to a V, you have to use the chain rule. So let's use the chain rule.

为了把这里的p变成,我们需要利用链式法则,好，让我们使用链式法则。

麻省理工公开课 - 热力学与动力学课程节选

Now you have to know from elementary calculus that v times dv/dt is really d by dt of v square over 2.

根据初等微积分知识你们得知道,v乘以dv/dt其实就是d/2)/dt

耶鲁公开课 - 基础物理课程节选

So you know your cycle, you know, you could have a whole complicated sequence on a p v diagram of steps going back.

因此，对某一的循环过程，可以在pV图上画出,一系列很复杂的小步骤。

麻省理工公开课 - 热力学与动力学课程节选

You know that if you took a derivative of this, you will find v of t is v0+at.

如果你对这个式子求一次导,你将会得到v=v0+at

耶鲁公开课 - 基础物理课程节选

Now, I hope you guys know that much calculus, that when you take a derivative of a function of a function, namely v square over 2 is a function of v, and v itself is a function of t, then the rule for taking the derivative is first take the v derivative of this object, then take the d by dt of t, which is this one.

我希望你们了解更多的微积分知识,当你对复合函数求导时,也就是说v^/2是关于v的函数,而v本身是关于t的函数,求导的法则应该是,第一步是这一部分对v求导,然后v再对t求导,得到这一部分

耶鲁公开课 - 基础物理课程节选