我们再求一次导数，也就是对导数求导。
Let's sneak in one more derivative here, which is to take the derivative of the derivative.
微积分基本定理，不是曲线积分的，告诉我们，如果对函数的导数积分，就会得回原函数。
So, the fundamental theorem of calculus, not for line integrals, tells you if you integrate a derivative, then you get back the function.
这意味着，当我们对吉布斯自由能求它的变量，的偏导数的时候，我们会得到我们以前学过的东西。
So this means that they were taking the derivatives of the Gibbs free energy with respect to one of its variables is something that we should know.
把对压强的导数拿出来，看看有什么发生。
Let's take the derivative outside with pressure and see what happens.
你可以想象一下对它们继续求偏导数，将会得到很多偏导数，所以我们要，仔细考虑那时的情形。
You can imagine that if you keep taking partials you may end up with more and more, so we will have to figure out carefully what the condition should be.
这个类似于，力除以质量等于加速度，就是速度对t的导数。
That is the analog of force divided by mass equals acceleration, which is d over dt of velocity.
我们已经发现,它由f对x的偏导数给出。
Well, we have seen that it is given by the partial derivative f sub x.
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。
Remember, we take the derivative of the square. We take twice this quantity times the derivative of what we are squaring.
对n的偏导数，这里的n是摩尔数。
对他来说，研究矢量的导数是很有趣的事。
It is interesting for him to study the derivative of a vector.
采用矩阵迭代法可以直接迭代计算特征向量导数，避免了对奇异灵敏度方程的求解。
Using matrix iteration methods, the eigenvector derivatives can be iterated directly, solving the singular sensitivity equation can be avoided.
事实上，这个方程给出的是，u对t的偏导数。
And, in fact, what the equation will give us is the derivative of u with respect to t.
这就是说，可以很简单的写出dG在，恒定压强下对温度的偏导数，是负。
That is, it's easy to write down straight away that dG with respect to temperature at constant pressure s is minus s.
选择任意两个分量，假定是x和，你得到fx对z的偏导数，对x的偏导数，the，partial，of，the，z，component，with，respect，to，x,让它们相等，对于任意一对变量做同样的事情。
z You pick any two components, say the x and the z component, and you take the partial of the x component with respect to z, fz and you must make them equal. And the same with every pair of variables.
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？
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?
利用相关系数在真实匹配点附近的统计特性，通过对相关系数进行曲线拟合，根据其一阶导数确定最大相关系数所在的位置，快速得到亚像素匹配点。
By using the statistic properties of the correlation coefficient, a curve correlation coefficient is calculated, and then the matching point is obtained through evaluating it's derivative function.
曲率又是位移的二阶导数，同时曲率又与应变存在着一一对应关系。
The curvature is the second order derivative of displacement. Also, it has a liner relationship with stain.
在模拟的紊流风场中，应用这一方法对平板和江阴长江大桥的节段模型进行了试验，识别了其气动导数。
A thin plate and the sectional model of the Jiangyin Bridge were tested in turbulent wind in a wind tunnel to extract their flutter derivatives.
其中，操纵水动力导数预报的精确程度无疑对整个船舶操纵性预报工作具有至关重要的影响。
The precision of the maneuverability hydrodynamic derivatives was undoubtedly of great importance to predict the ship maneuverability at the preliminary stage of ship design.
本文对主梁的颤振导数识别，采用与主梁颤振分析试验相同的节段模型和测量装置，以自由振动法进行试验。
This paper makes use of free vibration method, using the same model and measuring device to identify the flutter derivatives of the girder.
改进导数重构法的提出对混沌分析方法的实际应用有着重要意义。
The proposal improved derivative reconstruction method is significant to the practical application of the chaotic analysis method.
对利用差谱—二阶导数分光光度法直接测定强干扰基体中微量组分的原理和实验方法进行了探讨。
A new method for determining directly trace component in interfering base by absorbance subtraction -second derivative spectrophotometry is proposed.
通过挖掘可测同步误差中所隐含的信息对扩张系统的各个状态进行估计，从而实现了系统的输出及其导数的同步。
Synchronizing output of chaotic system and its derivatives is realized by collecting the information wrapped in observable synchronizing error to estimate the states.
本文对磨光函数的连续形式及离散形式给出了各阶导数的误差估计。
In this paper, error estimations on the derivatives of finite orders for continuous and discrete forms of smoothing functions, are given.
在控制方程的推导中，对黏弹性本构关系采用物质导数。
The governing equation was derived from the viscoelastic constitution relation by using material derivative.
对具有多重极点的有理函数，本文给出了部分分式展开的实用算法，该算法不需求导数值。
This paper gives a practical algorithm for partial fraction expansion of a rational function with multiple poles without derivative evaluation.
本文研究与其导数具有一个分担值对的整函数的唯一性问题。
This paper deals with problems of the uniqueness of entire functions that share one pair of values with their derivatives.
结果证明，导数分光光反法对痕量组分的测定是十分有效的。
It is tested that derivative spectrophotometer is very effective for determining trace components.
主要讨论了测量参数间的时间延迟对飞机气动导数辨识结果的影响。
This paper briefly discusses the effects on the aerodynamic derivative identification results caused by time delay in measured parameters.
主要讨论了测量参数间的时间延迟对飞机气动导数辨识结果的影响。
This paper briefly discusses the effects on the aerodynamic derivative identification results caused by time delay in measured parameters.
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