nth derivative of a quotient
by John from John D. Cook on (#756TM)
There's a nice formula for thenth derivative of a product. It looks a lot like the binomial theorem.
There is also a formula for thenth 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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