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And all this is, is saying that when you take a mixed second derivative, it doesn't matter in which order you take the two derivatives.
麦克斯韦关系的本质是,当你考虑混合的二阶导数时，求导的顺序不影响最后的结果,现在，我们利用这些关系。
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Unlimited leverage comes automatically with an option exchange. And derivative trading which made the option exchanges look like a benign event.
期权交易与无限杠杆率是与生俱来的,而且金融衍生品交易使得,期权交易看似有益。
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If you knew only the third derivative of the function, you can have something quadratic in t without changing the outcome.
如果方程里有三阶导数,你就可以引入一个二次项,但是结果却不会变
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The first derivative is more important than just the position of their regard for us, getting better and better.
态度的改观,比一开始对我们的看法更为重要，会越来越好。
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So, these two are equal to each other as well which tells me that this derivative, Cp dH/dT constant pressure is Cp.
所以这两者也相等,这告诉我们在恒压下微分，等于。
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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？
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But, of course, we want to go all the way to distance, so we take the second derivative and we have this equation for force here.
当然我们最后想要的是距离,所以我们取二阶微,分就有这个式子。
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He's just insisting that we cannot understand writing to be derivative.
他只是想说明我们不能将书写理解成为衍生物。
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All right, what we gonna do, we want to take a derivative of this thing.
接下来我们要求导了
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Conflict and war are primary. Peace is derivative.
冲突和战争是首要的，和平才是衍生物。
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What's a function, what's a derivative, what's a second derivative, how to take derivatives of elementary functions, how to do elementary integrals.
什么是函数,什么是导数,什么是二阶导数,如何对初等函数求导,如何进行初等积分
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I tell you something about the second derivative of a function and ask you what is the function.
我告诉你一个函数的二阶导数,然后问你这个函数是什么
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So now we have this derivative, in terms of physical quantities, things that we can measure.
现在我们得到了这个导数,它可以用实验可测的与。
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Then the second derivative gives the change in entropy with respect to the variable that we're differentiating, with respect to which is either pressure or volume.
二阶导数给出熵,随着变量变化的情况，这些变量包括压强或者体积。
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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。
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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
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If I can just have it there before me, that is a very difficult and derivative intellectual act, and it cannot be understood as primordial or primitive.
仅是面对着它，对于思维来说非常困难，并且这不能被理解为是原始的。
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To find a maximum I want the second derivative to be negative.
最大值处的二阶导数是负数
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The first derivative of their regard for us is positive. Okay?
他们对我们态度的转变首先是积极的，，对吧？
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But your real concern has been about the credit derivative market.
但是你真正关心的是,信用衍生品市场。
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And, so you propose that there is no, that this derivative is zero, and that the internal energy is given simply by this quantity.
你认为这是零，这个微分是零，内能仅仅由,这个简单的量决定。
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And all we did, further, is take that second derivative.
总而言之，我们所做的就是求二阶导数。
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So the slope of the guess is the first derivative.
因此斜率等于此处的一阶导数。
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And I can take this derivative.
我们这样求导。
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Why is the derivative of a vector also a vector?
为什么矢量的导数还是一个矢量呢
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Good, take a derivative and Set it equal to zero.
好的,求导,然后呢,令它等于0
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The Joule experiment was a constant energy experiment, right. Here we're going to have to find a constant enthalpy experiment, and that is going to be the Joule-Thomson experiment. That's going to extract out a physical meaning to this derivative here.
非常像焦耳实验,焦耳实验是一个能量恒定的实验,我们这里要做的是，找到一个焓不变的实验,也就是焦耳-汤姆逊实验,这个实验可以把这里的微分式形象化。
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Change the independent variable, find the change in the function, take the ratio and that's the derivative.
改变自变量,算出函数的变量,计算比值,这就是求导
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We have discovered that this partial derivative that appears in the definition, the abstract definition of the differential for internal energy, is just equal to the constant volume heat capacity.
我们还发现,这个偏微分出现在了，内能的偏微分,定义式中，它也就是热容。
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