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.

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结果表明 ：方程中混合偏导数项系数具有控制网格正交性的作用；

The factor of the mixed partial derivative term controls the grid orthogonality. The other two factors of second order partial derivative terms control the grid spacing.

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海森矩阵被应用于牛顿法解决的大规模优化问题。混合偏导数和海森矩阵的对称性海森矩阵的混合偏导数是海森矩阵非主对角线上的元素。

Hessian matrices are used in large-scale optimization problems within Newton-type methods because they are the coefficient of the quadratic term of a local Taylor expansion of a function.

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But, of course, it's going to come from the fact that these second derivatives are also equal.

但是，结果同样是依赖于,二阶混合偏导数相等。

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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。

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So, using those, now, what happens if we take the second derivative of A, the mixed derivative, partial with respect to T and the partial with respect to V.

如果我取A的二阶导数,混合导数，对T偏微分,再对V偏微分。

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