来自《耶鲁大学开放课程：基础物理 第6集 第6集》

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  It comes from the fact,
  那我告诉大家怎么推导
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  if you start at some point and you go to another point
  如果你从一点开始向另一点移动
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  and you ask for the change in the function,
  你想求出函数的变化量
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  the change is accumulating as you move.
  函数的变化量随着你的移动而不断积累
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  You can move horizontally and then vertically,
  无论你是先水平移动后竖直移动
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  or you can move vertically and then horizontally.
  还是先竖直移动后水平移动
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  The change in the function is a change in the function.
  函数的变化量就是这么多
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  You've got to get the same answer both ways.
  通过两种方法得出的结果是一样的
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  That's the reason;
  这就是原因
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  that's the requirement that leads to this requirement.
  也就是它成立的前提条件
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  Now, I will not be keeping track of functions
  对于今天会讲到的函数
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  to this accuracy in everything we do today.
  我就不会再这么详细地分析了