它只有关于每个变量的偏导数。
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.
好的，那就是偏导数的定义。
我们还要试图理解偏导数。
因此，我们应该重新理解偏导数的含义。
So, we have to figure out what we mean by partial derivatives again.
当遇到偏导数时，一定记住，不能约分。
Somehow, when you have a partial derivative, you must resist the urge of simplifying things.
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.
我是说现在已经有两个一阶偏导数。
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.
对n的偏导数，这里的n是摩尔数。
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?
同样地，梯度也是把偏导数糅合到一起。
Well, the gradient is also a way to package partials together.
那么dx和dy前面的系数就是偏导数。
设，在上有连续的偏导数。
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.
我们说一个函数是可微的，如果这些偏导数存在。
And, we say that a function is differentiable if these things exist.
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.
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.
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.
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.
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.
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