临界点是，偏导数都为零的点。
So, critical points, remember, are the points where all the partial derivatives are zero.
对于任意两分量，混合偏导数相等。
For every pair of components the mixed partials must be the same.
我们首先要做的事是,求偏导数，fx是多少？
What we would start doing immediately is taking the partial derivatives. What is f sub x?
那么dx和dy前面的系数就是偏导数。
首先考虑第一个分量，求出它关于x的偏导数。
Ry-Qz Well, so we have to take the first component, Ry minus Qz, and take its partial with respect to x.
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.
未知量是一个函数，这个方程，将把函数的偏导数联系起来。
So the unknown is a function, and the equation will relate the partial derivatives of that function to each other.
我们还学过微分的链式法则，也就是用其他量来代替这些偏导数。
So, we've learned about differentials and chain rules, which are a way of repackaging these partial derivatives.
多元函数的连续性，偏导数，方向导数及可微性之间的关系。
The Relation between the Continuity, the Partial Derivatives, the Directional Derivatives and the Differentiability of a Function.
其实还有其他不是极值点,但偏导数为0的点，我们来给这样的点起个名。
There are actually other kinds of points where l the partia derivatives are zero. Let's give a name to this.
现在可以看到，全微分里面的这些偏导数系数，都可以用一个变量表示出来。
Now you see how the total differential accounts for, somehow, all the partial derivatives that come as coefficients of the individual variables in these expressions.
针对对称导数、对称偏导数，给出了一些新形式的微分中值定理。
In this paper, symmetric derivative and symmetric partial derivative are researched and some new differential mean value theorems are defined.
而且在整个推导过程中，对于全导数和偏导数的概念没有分清楚。
And in the process of producing the concepts of the total derivative and the partial derivative are confused.
在此基础上提出了基于布尔偏导数的组合电路双故障检测的新方法。
Then, a new method testing the double fault of combinational circuits based upon Boolean partial derivative is proposed.
对多元有限离散函数引入了偏导数及微分新概念，并讨论了其性质。
The partial differentiations and derivatives are introduced for multivariate finite discrete functions, and the properties of which are discussed.
第三部分讨论最高阶偏导数项具有时滞的变分不等式的最优控制问题。
Finally in the third part, we study the optimal control problems for the variational inequality with delays in the highest order spatial derivatives.
我现在所要做的一切就是，考察自由能对，温度，体积和压强的偏导数。
So, all I want to do now is look at the derivatives of the free energies with respect to temperature and volume and pressure.
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.
运用误差理论和偏导数原理，推导出转位误差与寻北误差二者之间的关系模型。
The mathematical model between position error and north seeking error is gotten through error theory and partial derivative principle.
但是有一件事情，我必须指出来，在现实中，很多函数的偏导数之间，存在着很好的关系。
But one thing at a time. I wanted to point out to you that very often functions that you see in real life satisfy many nice relations between the partial derivatives.
目前的灵敏度分析往往需要依赖于某种寻优算法，并要求目标函数能求取偏导数。
At present, the method of sensitivity analysis depends on a algorithmic optimization, and asks to be can compute differential coefficient of the target function.
计算偏导数的办法没这么麻烦，因为我们有常规的方法，因此我们不需要通过定义去求偏导数。
And, we'll actually learn how to compute their partial derivatives without having to do this because we'll just have the usual methods for computing derivatives.
本文利用一条等熵参考线和两个等焓偏导数建立了火箭发动机性能参数的外推公式。
In this paper, the extrapolation formulas of rocket engine performance parameters are established utilizing one isentropic reference line and two partial derivatives for fixed enthalpy.
网络成批训练，使得权重矢量和偏导数矢量都同时与所有训练矢量的变化成正比地改变。
Batch training of network makes weight vectors and its partial derivative vectors proportionally follow the change of all training vectors.
在频域灵敏度分析中，利用计算线性代数系统的偏导数的纯代数方法是简单和有效的。
Purely algebraic methods for computing the sensitivity of linear algebraic system have been proven to be simple and effective in the frequency domain.
有一个极值问题，也有关于拉格朗日乘数法的，链式法则也会有的,约束条件下偏导数当然不会漏掉。
Expect one about a min/max problem, something about Lagrange multipliers, something about the chain rule and something about constrained partial derivatives.
新算法不需提供非线性方程的偏导数，但可利用近似偏导数指导搜索方向，提高搜索效率。
The new algorithm could use differential information to guide searching direction without providing derivatives, so as to simplify fitting process and raise searching efficiency.
所用的可靠度计算公式直接在基本变量空间中求解，避免了繁琐的求偏导数和正交变换工作。
The formula of reliability index is calculated in the origin space directly, so derivation and orthogonal transformation are avoided.
本文采用有限元法，利用压力参数法和偏导数法直接推求分块可倾瓦导轴承的动力特性系数。
The dynamic coefficients of tilting pad guide bearings are derived with the help of finite-elements using pressure parameters partial differentiation.
该文的方法适用于求取较为简单的二维逆z变换问题，尤以偏导数法和逆卷积法更具实际意义。
So the methods given in this paper can be used to get some simple inverse Z transform. The partial derivative method and deconvolution method are of practical use.
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