来自《耶鲁大学开放课程：基础物理 第6集 第6集》

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  Then, I can also take d^2 f / dy·dx.
  当然我也可以求 d^2 f / dy·dx
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  That means, take the y derivative of the x derivative,
  就是对 x 求导的结果再次对 y 求导
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  but here's the x derivative, take the y derivative of that,
  这里是对 x 求导的结果 对它再次对 y 求导
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  put a 2·y there, and I get 6·x^2·y.
  那里得到 2·y 结果是 6·x^2·y
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  So, you're supposed to notice something.
  这里你应该发现点什么了
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  If you already know this, you're not surprised.
  如果你早知道的话 就不会惊讶了
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  If you've never seen this before,
  如果你从没见过的话
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  you will notice that the cross derivative,
  你会发现交叉求导的结果
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  y followed by x and x followed by y,
  不管先对 x 还是先对 y 求导
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  will come up being equal.
  结果都是相同的
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  That's a general property of any reasonable function.
  这是一般函数的共性
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  By reasonable,
  我说一般的意思是