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。
So, the definition will take effect. The acceleration is as a vector, and the acceleration vector is just the derivative of a velocity vector.
有必要对加速度给出一个严格的定义，加速度,作为一个矢量,是速度的一阶导数。
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。
We've done this before-- this is the conservation of energy, and in order to find the period of the simple harmonic oscillation, we take the time derivative.
以前算过-,这是能量守恒，为了算出,简谐振荡的周期，我们求时间导数。
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？
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。
Wxx If I take the second derivative with respect to x and x so first I want to take maybe the derivative with respect to x Wx But first, let's take the first partial, Wx That will be 2ax by, right?
如果我要求二阶偏导数,首先要求关于x的一阶偏导数,让我们首先求出,它等于2ax+by，对吧？
One way to think about this intuitively if the derivative is very large the function is changing quickly, and therefore we want to take small steps.
关于这个方法很直观的一点想法是，如果导数非常大，函数也就变化的非常快，因此我们想一小步一小步的来。
All right. If the derivative is small, it's not changing, maybe want to take a larger step, but let's not worry about that all right?
好，如果导数很小的话，函数就基本没什么变化，可能我们就想把步子迈大一点儿了，但是别为这个担心？
For example, if you write a story based upon another book or take a photograph of a painting, even though you created a new work, it could be what is known as a derivative work and infringement.
例如，你写的故事是基于另一本书，或者对着一幅画拍了张照片，尽管你创作了一些新的东西，但是这会被认定为衍生著作，并且是侵权的。
So one way to get a small change in temperature is to take a derivative with respect to temperature.
所以得到温度微小变化的一种方法，就是对温度求导。
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。
It is the same thing as, in one variable calculus, when you take the anti-derivative of a function it is only defined up to adding the constant.
相当于在一元微积分中，取一个函数的不定积分，仅仅需要在结果后加一个常数。
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。
That is, if we take the derivative G of delta G of mixing the partial derivative with respect to pressure, at constant temperature, of course, there's no explicit pressure dependence.
就是说，如果我们对,混合物的△,对压强求导，温度不变，当然，不是对压强的显函数。
And what that says is that the heat capacity and of course we could take the limit of this, but we can just take the derivative of this with respect to temperature more easily.
那意味着热容，当然我们也可以做它的极限，但我们用它，对温度求导更容易些。
I'm going to take the time derivative just as I did in the case of the spring.
我将要提取时间，就像我在，弹力那个例子里那样。
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。
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。
You take the y component, take the derivative with respect to x, take the x component, differentiate with respect to y, you should get the same answer. And that is important to know.
对y分量，关于x求导，对x分量，关于y求导，应该得到相同结果，这个知识点很重要。
Take the accumulator - also known as the "I'll kill you later" - financial derivative.
以蓄电池-来作为以后我会杀了你” -金融衍生工具。
Look for derivative areas of economic growth and take a 12 - to 25-year horizon.
寻找经济增长的衍生领域，并为12-25岁的视野。
Secondly, the new generalized gradient is introduced to take advantage of the given directional derivative.
其次讨论了一类新的广义梯度，这样的广义梯度能够充分利用已经有的方向导数的信息。
Secondly, the new generalized gradient is introduced to take advantage of the given directional derivative.
其次讨论了一类新的广义梯度，这样的广义梯度能够充分利用已经有的方向导数的信息。
应用推荐