Fractional Calculus
 

f(x,0)=x^a
f(x,1)=ax^(a-1)
f(x,2)=a(a-1)x^(a-2)
f(x,n)=a(a-1)(a-2)...(a-n)x^(a-n)

This is of course the n'th derivative function for x^a. Now do you see why I wanted the previous two problems solved? ;)

It should be very clear if you read the previous two topics that I want not only solutions for non-negative integer values of 'n' but also for non-negative real values. The idea is to extend my calculus tools' abilities.

Note 1: Not all f(x) with f'(x) has more than the whole number solutions? I'll have to do more research before I can say that definitively!
Note 2: I originally called this 'recursive derivatives' because of the frist paragraph but found references to 'fractional calculus' at Wikipedia. This matches the overall post.

[url]http://en.wikipedia.org/wiki/Differintegral[/url]

specifically, I think this is what you want (where [tex]\alpha[/tex] is your n)

Holy calculators Batman - someone actually replied! ;)
Yeah, that's another good article on Wikipedia for this subject. 'Fractional calculus' is kind of a misnomer since real values are allowed as well.

I was working from the derivative point of view, but according to those articles the derivatives are sometimes actually worse than integrals.