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。

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I take a look at the second derivative, which is the second order condition.

我需要求出二阶导数,即需要寻找二阶条件

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And the point is that the second derivative of A, with respect to V and T in this order is the same as the second derivative of a with respect to T and V in this order.

问题的关键在于A的二阶导数，对V和T以这样一个顺序求导,和对T和V以这样一个顺序,求导是一样的。

麻省理工公开课 - 热力学与动力学课程节选