⚙️ 工程
商的 n 阶导数公式nth derivative of a quotient
文章介绍了商函数（即两个函数的比值）的 n 阶导数的计算公式，该公式比乘积函数的 n 阶导数更复杂且鲜为人知。作者通过将商法则以非传统方式表达，并应用两次商法则推导出结果，揭示了这一高阶微分运算的结构特征。
John
There’s a nice formula for the nth derivative of a product. It looks a lot like the binomial theorem.
There is also a formula for the nth derivative of a quotient, but it’s more complicated and less known.
We start by writing the quotient rule in an unusual way.
Applying the quotient rule twice gives the following.
And here’s the general rule in all its glory.
Source: V. F. Ivanoff. The nth Derivative of a Fractional Function. The American Mathematical Monthly, Vol. 55, No. 8 (Oct., 1948), p. 491
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