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.
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.
科学计算及其应用常常需要多变量函数的有关偏导数问题的计算，通常使用的计算方法是符号微分或差分近似。
Evaluation relevant to the partial derivatives of the multivariable functions is often done in scientific computation, usually by means of the symbolic differentiation or the divided difference.
模型响应对电阻率及介电常数的偏导数用格林函数和互换原理计算。
The partial derivatives of the electromagnetic responses with respect to resistivity and dielectric parameter are calculated by using Green function based on reciprocity principle.
本文建立了多元复合函数的二阶偏导数公式。
In this paper, the formula of partial derivative of second order on compound function of many varables is established.
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.
探讨二元函数的连续性、偏导数、方向导数以及可微性之间的关系，有助于我们对二元函数的学习。
A discussion of the relations between continuity, partial derivative, directional derivative and differentiability of binary function is helpful for us to study binary function.
通过研究三角形多面体模型节点偏导数的计算方法，对目标函数进行线性化处理，形成了计算机自动迭代修改模型体的技术。
By researching the partial derivative calculation of model vertex and linearity treating field function using Taylor series, the 3D models can be changed via automatic optimization;
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.
偏微分方程就是，跟函数各个偏导数有关的方程。
A partial differential equation is an equation that involves the partial derivatives of a function.
以中值定理为工具，给出了利用一阶偏导数判定二元函数极值的方法。
The criterion extreme value of binary function for first partial derivative is given by means of the mean value theorem. The two theorems are obtained.
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.
应用函数列的极限与函数的极限交换次序定理，研究了二元函数的二重极限与它的两个累次极限的关系定理，研究了二元函数的两个二阶混合偏导数可交换次序定理。
By using the limits of functions and the exchange limit theorem, we considered the relationship between the double limit of function with two variables and its repeated limits.
利用多元函数极值的定义和偏导数的定义公式证明二元函数与一元函数在某点取得极值的关系。
This article use the diverse function extremum and the local derivative's definition formula to prove the relation between extremum obtained by the two function and the dollar function at some point.
在一元函数广义导数定义的基础上，提出了多元函数广义偏导数的概念，相应地建立了广义偏导数的运算规则，获得了有关的一些性质。
Concept and operation rules of generalized partial derivative of multivariate function are given basis on generalized derivative of single variable function in this paper.
通过在积分换元、微分方程求解、多（一）元复合函数求全微分、偏导数及高阶偏导数中的应用举例，论述了一阶微分的形式不变性在微积分学中的作用不应被忽略。
Based on the theory of differential geometry and geodesy, the second order differential equation and the first differential relationship are derived on the regional earth ellipsoid in this paper.
通过在积分换元、微分方程求解、多（一）元复合函数求全微分、偏导数及高阶偏导数中的应用举例，论述了一阶微分的形式不变性在微积分学中的作用不应被忽略。
Based on the theory of differential geometry and geodesy, the second order differential equation and the first differential relationship are derived on the regional earth ellipsoid in this paper.
应用推荐