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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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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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You know that if you took a derivative of this, you will find v of t is v0+at.
如果你对这个式子求一次导,你将会得到v=v0+at
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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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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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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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And the mathematics of that equation involved a double derivative in time of x 0 plus some constant times x equals zero with some constraints on it.
那个数学方程式,包括了x对时间的二阶导数,加上常数乘以x等于,还有一些限制条件。
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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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Take a derivative of S1.
求出S1的导数
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I would say, okay, this guy wants me to find a function which reduces to the number a when I take two derivatives, and I know somewhere here, this result, which says that when I take a derivative, I lose a power of t.
出题者想要我找出一个函数,它在经过两次求导后得到数字a,我知道这里的某个地方,这个结论告诉我,我每求一次导,t就降一次幂
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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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I take a look at the second derivative, which is the second order condition.
我需要求出二阶导数,即需要寻找二阶条件
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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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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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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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It is in fact a very, very difficult and derivative act of the mind to try to forget that I am looking at a sign that says 'exit' and, in fact, just looking at what is there without knowing what it is.
事实上，试图忘记那个写着存在的标志,和只知道它存在而不知道它是什么，是非常难的事情。
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Even though we started with a single vector, which is the position vector, we're now finding out that its derivative has to be a vector and the derivative of the derivative is also a vector.
即使我们从单个矢量出发,即位移矢量,我们现在也能得出它的导数是矢量,而且导数的导数也是一个矢量
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So I differentiated this object, this is my first derivative and I set it equal to 0 Now in a second I'm going to work with that, but I want to make sure i'm going to find a maximum and not a minimum, so how do I make sure I'm finding a maximum and not a minimum?
这样我就对它求出导数了,这是一阶导数,令它等于0,一会我们就要计算了,但我先确定一下是最大值还是最小值,我怎么确定是最大值还是最小值呢
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So, using those, now, what happens if we take the second derivative of A, the mixed derivative, partial with respect to T and the partial with respect to V.
如果我取A的二阶导数,混合导数，对T偏微分,再对V偏微分。
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You can take a derivative of the derivative and you can get the acceleration vector, will be d^2r over dt^2, and you can also write it as dv over dt.
你可以对导数再求一次导,你就可以得到加速度矢量,也就是 d^2 r / dt^2,你也可以写成 dv / dt
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Now, I hope you guys know that much calculus, that when you take a derivative of a function of a function, namely v square over 2 is a function of v, and v itself is a function of t, then the rule for taking the derivative is first take the v derivative of this object, then take the d by dt of t, which is this one.
我希望你们了解更多的微积分知识,当你对复合函数求导时,也就是说v^/2是关于v的函数,而v本身是关于t的函数,求导的法则应该是,第一步是这一部分对v求导,然后v再对t求导,得到这一部分
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If you know the second derivative of y to be a, then the answer looks like this.
如果你知道y的二阶导数是a,那么这就是答案
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And the point is that the second derivative of A, with respect to V and T in this order is the same as the second derivative of a with respect to T and V in this order.
问题的关键在于A的二阶导数，对V和T以这样一个顺序求导,和对T和V以这样一个顺序,求导是一样的。
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In other words, your job is to guess a function whose second derivative is a, and this is called integration, which is the opposite of differentiation, and integration is just guessing.
换言之,你的任务是要猜出一个二阶导数为a的函数,这就是积分,和微分恰恰相反,积分就是猜
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If you want to know how fast it's moving at a given time, if you want to know the velocity, I just take the derivative of this answer, which is 10-10t.
如果你想知道它在给定时刻的运动有多快,如果你想知道它的速度,我只要对这个式子求导,得到10-10t
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take the derivative of this, get the velocity vector and you notice his magnitude is a constant Whichever way you do it, you can then rewrite this as v square over r.
对这个式子求一次导,就能得到速度矢量,你会发现其模长是常数,不管用什么方法,加速度也可以写成 v^2 / r
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OK, so for a constant volume process, du we can write du, partial derivative of dT u with respect to T at constant V, dT, dv plus partial derivative of u at constant V, dV.
好，对于一个恒定体积的过程，我们可以写出,等于偏u偏T，V不变，加上偏u偏V，T不变。
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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
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