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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I actually need to check the second order condition.

实际上我们还需要验证二阶条件

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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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You've learnt what the words mean, but you have abstract and unconscious rules that take these words, figure out the order, and in a fraction of a second, give rise to understanding.

虽然你已经知道了这些单词的意思,但却是你所拥有的抽象且无意识的规则,让你认清单词,确认语序,然后在一瞬间让你理解整个句子

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In my in my area of research, it's common for us to want to process about 100 images a second in order to get real time display. Each image has about a million elements in it. I 've got to process about a half a gig of data a second in order to get anything out of it.

在我们的研究领域内，我们经常要在一秒钟内处理大概,100张图片以获得实时显示,每个图片大概包括了100万像素,因此我必须在1秒内,处理半个G的数据,来获取我想要的。

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So how do I check the second order condition?

怎样验证二阶条件呢

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I differentiate a second time and check the sign, so the second order condition, I differentiate this expression again with respect to q1.

我们对它进行二次求导然后看符号,这个式子的二阶导数,就是一阶导数再对q1进行求导

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So if we differentiate this object, I'm gonna find a first order condition in a second.

想要求它的导数,先让我想想一阶条件

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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。

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