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词汇 Mixed partial derivative
分类 英语词汇 英语翻译词典
释义

Mixed partial derivative

中文百科

二阶导数的对称性 Symmetry of second derivatives

（重定向自Mixed partial derivative）

数学中，二阶导数的对称性（也称为混合导数的相等）指取一个n元函数

f(x_{1},x_{2}, \dots ,x_{n})

的偏导数可以交换。如果关于x_{i}的偏导数用一个下标i表示，则对称性断言二阶偏导数f_{ij}满足等式

f_{ij}=f_{ji}

从而它们组成一个n×n 对称矩阵。有时这也称为杨定理（Young's theorem）。

英语百科

Symmetry of second derivatives 二阶导数的对称性

（重定向自Mixed partial derivative）
The function f(x,y), as shown in equation (1), does not have symmetric second derivatives at its origin.

In mathematics, the symmetry of second derivatives (also called the equality of mixed partials) refers to the possibility under certain conditions (see below) of interchanging the order of taking partial derivatives of a function

of n variables. If the partial derivative with respect to x_{i} is denoted with a subscript i, then the symmetry is the assertion that the second-order partial derivatives f_{ij} satisfy the identity
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