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And what's fallen out when we do that, because in each case, one of the first derivatives gives us the entropy.
当我们这样做时就得到了结果，因为在这些例子中，一阶导数是熵。
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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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Can the strength of numbers, as well as respect for reason and a better argument be, ? in some sense, harmonized?
大众的力量，与尊重理性,及进阶辩论，能和谐共处吗？
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Okay, good, so what we're going to do is we're going to differentiate this thing to find a first order condition.
好吧,那我们接下来,对它求导后找出一阶条件
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So let me go ahead and pull up the staff solution 15 to the standard edition for a moment, the game is called 15, it takes one command line argument which is the dimensions of the board 3 by 3, 4 by 4, I'll do it 4 by 4.
下面我们继续,等一会儿，我会给出标准的解答，这个游戏叫做，有一个命令行参数，标识其大小是,3阶还是4阶，我选择4阶。
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Above some temperature is going to be positive, below some temperature is going to be negative.
低于这一温度它是负数，我们一般忽略这些高阶项。
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On the inside are the rungs or the struts that hold the ladder together.
梯子内侧是梯阶,也可以说是梯阶把梯子连接在一起
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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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So I'm hoping you guys are comfortable with the notion of taking one or two or any number of derivatives.
我希望你们,能习惯求一阶,二阶,或者任意阶导数的概念
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I think the main reason is that there are no equations that involve the third derivative explicitly.
我想主要原因是因为还没有等式,明显涉及三阶导数
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So if we differentiate this object, I'm gonna find a first order condition in a second.
想要求它的导数,先让我想想一阶条件
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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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Of course, you can take a function and take derivatives any number of times.
当然,你可以随意拿一个函数,对它求任意阶的导数
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This was a first order condition or a first order necessary condition.
这个只是一阶条件,是必要条件
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Normally, I will give you a function and tell you to take any number of derivatives.
通常情况下,我会给你一个函数,然后让你求任意阶的导数
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There are several things that you'll notice about the struts in this particular cartoon.
你们会注意到卡通模型上的,这些梯阶有些特别之处
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So here it is, I've got my first order condition.
到这里我满足了一阶条件
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One is that there's four different colors and so you can see red, blue, yellow, green here - four different colors and that's all there are, there aren't more than four.
一是这些梯阶有四种不同颜色,你可以看到红 蓝 黄 绿,恰恰只有四种不同颜色,不多不少
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Interestingly, only the first two derivatives have a name.
有趣的是,只有前两阶导数有名字
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Once you can take one derivative, you can take any number of derivatives and the derivative of the velocity is called the acceleration, and we write it as the second derivative of position.
只要你能求一阶导数,你就能求任意阶的导数,速度的导数被称为"加速度",我们把它写成位移的二阶导数
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that expresses the will of the majority, the will of the greater number be rendered compatible with the needs of philosophy and the claims to respect ? only reason and a better argument?
众人意志的民主，及大多数人的意志,能够兼容,哲学需求,及尊重理性,及进阶辩论的诉求吗？
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The first one is velocity, the second one is acceleration.
一阶导数叫速度,二阶导数叫加速度
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It's the phosphate and the pentose that make up the backbone - that make up the upright struts of the ladder and it's the bases that make up the connecting struts, so the bases are the colors.
磷酸基和戊糖,共同构成了主链,主链又构成了梯子上下的支柱,而碱基,则构成连接支柱的梯阶,碱基是用各种颜色表示的
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That there are two colors per strut, so what's linking the two backbones together are two colored segments that come from the outside towards the middle, and that the colors occur only in certain combinations, red and green, yellow and blue, that's all you see.
每个梯阶有两个颜色,主链是由,两种不同颜色的片段由外向内连接起来的,这些颜色仅以某种特定方式配对,红连接绿,黄连接蓝,大家都能看到
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These are the things that we do best and where we have advanced course work available in these three categories and so I'm going to emphasize these three but we'll talk about all of these subjects as we go through the course.
这是我们做的最好的三个方向,在这三个方向下我们开设有高阶的课程,因此我会重点讲这三个方向,但随着课程的进行,所有的主题我们都会讲到
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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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Well, unfortunately, we know this is not the right answer, because if you take the first derivative, I get 2t.
遗憾的是,我们知道这还不是正确答案,因为如果对它求一阶导数,会得到2t
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To make this a first order condition, I'm going to say "at the best response," put a hat over the 1.
为了达到一阶条件,我说在最佳对策下,在S1上写个帽
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It tells me that the best response to S2 is the ?1 that solves this equation, that solves this first order condition.
我们得出S2的最佳对策是?1,?1是这个方程的解,它满足一阶条件
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I differentiate a second time and check the sign, so the second order condition, I differentiate this expression again with respect to q1.
我们对它进行二次求导然后看符号,这个式子的二阶导数,就是一阶导数再对q1进行求导
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