Let's sneak in one more derivative here, which is to take the derivative of the derivative.
我们再求一次导数，也就是对导数求导。
Crack is a highly potent and addictive derivative of cocaine.
强效纯可卡因是一种药效极强、容易使人上瘾的可卡因制剂。
我们叫他f的导数。
It is the derivative of revenue pq with respect to quantity.
它是收入Pq相对于数量的导数。
And angular acceleration is the derivative of angular velocity.
角加速度等于，角速度的导数。
And now we have to take the derivative of this quantity squared.
现在我们要对这个量的平方求导。
And, we've also learned about acceleration, which is the derivative of velocity.
我们还学过加速度，也就是速度向量的导数。
So, the velocity vector is the derivative of a position vector with respect to time.
速度向量，是位置向量关于时间的导数。
If we take the example of the cycloid, well, what's the derivative of one minus cos?
以摆线为例，1，-，cos的导数是什么？
And, in fact, what the equation will give us is the derivative of u with respect to t.
事实上，这个方程给出的是，u对t的偏导数。
If I match this with equation two then that will tell me what the derivative of g should be.
如果把这个和方程比较,我能得到g的导数。
So, whenever I see dx, I will replace it by, well, -sin the derivative of cosine is negative sine.
当我看到dx，就把它替换成cos的导数，也就是。
You can also require that any derivative of your work be shared in the same way as the original.
还可以要求对作品的派生物使用与原版一样的条款。
Before we do that, since what we're after is the derivative, let's take the derivative of both sides.
在我们开始之前，因为我们需要的是导数，取方程两边的导数。
Gold is not a living thing, just a door stop throwing off nada, a derivative of our weakening dollar.
黄金并不是个活物，它只是弱势美元的衍生结果。
And so I can substitute that in there, and so I get that the power is the derivative of this versus time.
所以我可以代入这里，得到那个功率，是相对时间的衍生物。
So let's take the derivative of this with respect to total pressure. Well, this isn't total pressure.
对这个方程两边对总的压强求导，好，这里不是总压强。
The idea was panned in the Chinese state-run media as vague and largely derivative of [gm99nd] concepts.
中国官方媒体称这一构想含糊不清，是[gm66nd]概念的中国翻版。
However, in 1919, kerosene production was surpassed by that of gasoline, another derivative of petroleum.
然而，1919年，另一石油衍生产品——汽油产量超过煤油。
Then we can take the derivative of that quantity, when we vary the temperature, holding the volume constant.
即恒定体积，改变温度，这里恒定温度下。
I mean, acceleration is also going to be along the line, and it's going to has to do with the derivative of speed.
我的意思是加速度只沿这一个方向，它只要对速率求导即可。
Remember, we take the derivative of the square. We take twice this quantity times the derivative of what we are squaring.
还记得吧，对一个量的平方求导，就得到这个量的2倍，乘以这个量的导数。
I'm sure you remember some of the simpler rules for differentiation and could quickly tell me that the derivative of x2 is 2x.
我确信你们仍然记得一些简单的规则，并且能够迅速地告诉我x2的导数是2x。
Torque divided by moment of inertia is what will cause the angular acceleration, namely the derivative of angular velocity.
扭矩除以转动惯量,就会引起角加速度，也就是角速度的导数。
The chemical potential from the fundamental equation up here is the derivative of a with respect to the number of particles.
化学势，从基本方程上说，就是A对N的偏导，因此对A取N偏导，因此化学势也能，用正则配分函数表示。
What I showed you at the beginning, and then erased, basically justifies how to take the derivative of a reciprocal function.
最开始我讲过了，如何对倒数函数求导。
Yes, I divide... m Oh, there's an m here, m And now what I'm going to do, I'm going to take the time derivative of this equation.
对，我除以。，哦，这里有个，应该在这里。，and, the,m, has, to, be, here。，现在我要做的，我将把这个等式，转化成与时间有关。
See, if you took the derivative of this with respect to x you will get 2xy and this guy will go away x because there is no x in it.
如果你对它关于x求导,就会得到2xy，而这项就没有了,因为它里面没有。
See, if you took the derivative of this with respect to x you will get 2xy and this guy will go away x because there is no x in it.
如果你对它关于x求导,就会得到2xy，而这项就没有了,因为它里面没有。
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