'Happiness' is a derivative of 'happy'.
happiness是happy的派生词。
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。
我们叫他f的导数。
So we get rid of this derivative of g.
所以我们就消掉了G的微分。
The language is a derivative of plain Rexx.
此语言派生自普通的Rexx。
And I can take now the first derivative of this.
现在得到第一个推导式。
So, it's the second derivative of a position vector.
它是位置向量的二阶导。
That's the first derivative of the position versus time.
它就是位置，对时间的一阶导数。
It is the derivative of revenue pq with respect to quantity.
它是收入Pq相对于数量的导数。
Now, if we compare these two, we will get the derivative of h.
比较这两个，我们会得到h的导数。
And angular acceleration is the derivative of angular velocity.
角加速度等于，角速度的导数。
Well, it is given by the derivative of this with respect to u.
它由对u的偏导给出。
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。
So, product rule is OK for taking the derivative of a dot product.
那么乘积法则对点乘求导没问题。
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。
OK, now I have this derivative of the Gibbs free energy divided by the temperature.
现在要进行微分，对除以温度之后的吉布斯自由能。
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。
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。
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。
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。
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。
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。
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