来自《耶鲁大学开放课程：基础物理 第6集 第6集》

• 
  
  Now, you can take the y part, y^2,
  现在 就可以求 y 的部分了 y^2
• 
  
  yes, thank you.
  对 谢谢
• 
  
  Then, I can take df / dy, so then I look for y changes,
  然后求 df / dy 求出 y 的变化
• 
  
  this is 2·y here,
  这里是 2·y
• 
  
  so it's 2·x^3·y + 2·y.
  所以结果是 2·x^3·y + 2·y
• 
  
  so that's the x derivative and the partial y derivative.
  这就是对 x 和 y 的偏微分
• 
  
  Okay, so then you can now take higher derivatives.
  现在你就可以求高阶导数了
• 
  
  We know that from calculus and one variable,
  我们从一个变量的微积分那里知道
• 
  
  you can take the derivative of the derivative.
  可以对导数再次求导
• 
  
  So, one thing you can think about is d^2 f / dx^2,
  可以想到的就是求 d^2 f / dx^2
• 
  
  that really means take the d by dx of the d by dx.
  意思就是对 d / dx 再次对 x 求导
• 
  
  That's what it means.
  就是这个意思