⚙️ 工程
商的 n 阶导数公式及其复杂性nth derivative of a quotient
文章探讨了商函数的 n 阶导数公式，指出虽然积函数的 n 阶导数有类似二项式定理的简洁公式，但商函数的公式更为复杂且鲜为人知。作者通过将商法则写成一种特殊形式，并应用两次商法则推导出结果，展示了这个复杂公式的推导过程。
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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