So I'm hoping you guys are comfortable with the notion of taking one or two or any number of derivatives.

我希望你们,能习惯求一阶,二阶,或者任意阶导数的概念

耶鲁公开课 - 基础物理课程节选

Normally, I will give you a function and tell you to take any number of derivatives.

通常情况下,我会给你一个函数,然后让你求任意阶的导数

耶鲁公开课 - 基础物理课程节选

So if we differentiate this object, I'm gonna find a first order condition in a second.

想要求它的导数,先让我想想一阶条件

耶鲁公开课 - 博弈论课程节选

So the slope of the guess is the first derivative.

因此斜率等于此处的一阶导数。

麻省理工公开课 - 计算机科学及编程导论课程节选

The third derivative, unfortunately, was never given a name, and I don't know why.

遗憾的是三阶导数没有专门的名称,我也不知道这是为什么

耶鲁公开课 - 基础物理课程节选

Of course, you can take a function and take derivatives any number of times.

当然,你可以随意拿一个函数,对它求任意阶的导数

耶鲁公开课 - 基础物理课程节选

Interestingly, only the first two derivatives have a name.

有趣的是,只有前两阶导数有名字

耶鲁公开课 - 基础物理课程节选

Once you can take one derivative, you can take any number of derivatives and the derivative of the velocity is called the acceleration, and we write it as the second derivative of position.

只要你能求一阶导数,你就能求任意阶的导数,速度的导数被称为"加速度",我们把它写成位移的二阶导数

耶鲁公开课 - 基础物理课程节选

I differentiate a second time and check the sign, so the second order condition, I differentiate this expression again with respect to q1.

我们对它进行二次求导然后看符号,这个式子的二阶导数,就是一阶导数再对q1进行求导

耶鲁公开课 - 博弈论课程节选

Then, to find the meaning of b, we take one derivative of this, dx/dt, that's velocity as a function of time, and if you took the derivative of this guy, you will find as at+b. That's the velocity of the object.

接下来,为了弄清b的含义,我们取它的一阶导数,dx/dt,得到速度作为时间的函数,如果你对它求导的话,你会得到at+b,这就是物体的速度

耶鲁公开课 - 基础物理课程节选