And, as before, this comes from the fact that the mixed second derivatives are the same, no matter in which order you take them.

和以前一样，它来源于这样一个事实，混合二阶导数，求导次序改变，结果不变。

youdao

And all this is, is saying that when you take a mixed second derivative, it doesn't matter in which order you take the two derivatives.

麦克斯韦关系的本质是,当你考虑混合的二阶导数时，求导的顺序不影响最后的结果,现在，我们利用这些关系。

麻省理工公开课 - 热力学与动力学课程节选

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。

麻省理工公开课 - 热力学与动力学课程节选

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。

麻省理工公开课 - 热力学与动力学课程节选

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