来自《耶鲁大学开放课程：基础物理 第1集 第1集》

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  Now, multiply both sides by v.
  现在两边同时乘以v
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  Now you have to know from elementary calculus that
  根据初等微积分知识你们得知道
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  v times dv/dt is really d by dt of v square over 2.
  v乘以dv/dt其实就是d(v^(2)/2)/dt
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  Now, I hope you guys know that much calculus,
  我希望你们了解更多的微积分知识
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  that when you take a derivative of a function of a function,
  当你对复合函数求导时
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  namely v square over 2 is a function of v,
  也就是说v^(2)/2是关于v的函数
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  and v itself is a function of t,
  而v本身是关于t的函数
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  then the rule for taking the derivative
  求导的法则应该是
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  is first take the v derivative of this object,
  第一步是这一部分对v求导
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  then take the d by dt of t, which is this one.
  然后v再对t求导 得到这一部分
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  On the right-hand side, I'm going to write as a dx/dt.
  在等号右边 我要写成dx/dt
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  This much is standard.
  这么写很规范