nth derivative of a quotient

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. 491The post nth derivative of a quotient first appeared on John D. Cook.