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偏导数

n.partial derivative
网络partial derivatives; local derivative; partial differential coefficient

偏导数

偏导数

英-汉网络释义

偏导数

n.

1.partial derivative

1

A partial differential equation is an equation that involves the partial derivatives of a function .

偏微分方程就是，跟函数各个偏导数有关的方程。

2

So, we've learned about differentials and chain rules , which are a way of repackaging these partial derivatives .

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。

3

But, let's think of partial with respect to x , with respect to y, and with respect to z as the components of some formal vector .

但是，让我们考虑一个向量，其分量为对 x 的偏导数，对 y 的偏导数，以及对 z 的偏导数。

4

So, that's pretty easy . Plus, then we have the partial derivative, A little a times the rate of change of a in our situation.

这很简单，然后我们得到了偏导数，关于 a 的偏导数，formal，partial，derivative，，of，A，with，respect，to ，在这种情形下，a 的变化率。

6

In particular , the directional derivatives in the direction of I hat or j hat are just the usual partial derivatives .

特别地，在 i，j 方向的方向导数是，一般的偏导数。

7

So the unknown is a function , and the equation will relate the partial derivatives of that function to each other.

未知量是一个函数，这个方程，将把函数的偏导数联系起来。

8

So, critical points, remember, are the points where all the partial derivatives are zero .

临界点是，偏导数都为零的点。

9

Some preliminary applications of the partial derivative in proving inequalities are also given .

并给出了偏导数在不等式证明中的一些简单应用。

10

11

That's just the fact that the mixed second partial derivatives are equal.

这可以说明，二阶混合偏导数与次序无关。

12

Derivative with respect to total pressure , that's the molar volume of the liquid . The liquid .

化学势对总压强的偏导数等于液体的摩尔体积，液体的。

13

Another method for proving the three thermodynamical partial derivatives equaling chemical potential is given .

对三个热力学偏导数等于系统化学势给出了又一种证明方法。

14

Because these mixed second derivatives are the same thing.

因为这两个混合二阶偏导数，是相等的。

15

Returns the partial derivative of x with respect to the screen -space x-coordinate.

返回关于屏幕坐标 x 轴的偏导数

16

Well, we have seen that it is given by the partial derivative f sub x .

我们已经发现，它由 f 对 x 的偏导数给出。

17

OK , so that 's the definition of a partial derivative .

好的，那就是偏导数的定义。

18

That is , it's easy to write down straight away that dG with respect to temperature at constant pressure S is minus S.

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。

19

So , we have to figure out what we mean by partial derivatives again .

因此，我们应该重新理解偏导数的含义。

20

And, in fact , what the equation will give us is the derivative of u with respect to t .

事实上，这个方程给出的是，u 对 t 的偏导数。

21

Tomorrow we will see how to decide which one it is, in general, using second derivatives .

明天我们再讲如何用二阶偏导数，区分这三种点。

22

And, we say that a function is differentiable if these things exist .

我们说一个函数是可微的，如果这些偏导数存在。

23

OK, and so the coefficients of dx and dy are the partials.

那么 dx 和 dy 前面的系数就是偏导数。

24

And this is the derivative with respect to temperature .

这是吉布斯自由能对温度的偏导数。

25

What we would start doing immediately is taking the partial derivatives . What is f sub x?

我们首先要做的事是，求偏导数，fx 是多少？

26

There are actually other kinds of points where l the partia derivatives are zero. Let 's give a name to this.

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。

27

Generally , you would want all the partial derivatives , 0 no matter how many variables you have, to be zero at the same time.

通常情况下，所有的偏导数 —，无论有多少个自变量 ——都同时为。

28

For example , if we have a function of three variables, the vector whose components are the partial derivatives .

例如我们有一个三元函数，它的梯度向量的分量就是那些偏导数。

29

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