If I want to take the derivative of $ax^n$, I will get $anx^{n-1}$. If I were to take the derivative again, I get $an(n-1)x^{n-2}$.
We can generalize this for integer k easily to get the kth derivative $a\frac{n!}{(n-k)!} x ^{n-k}$. But what about for a more general k?
Does this have some name? Has it been widely studied? If so, can you show how to generalize this formula for kth derivative of $ax^n$, and explain how it works? If not, is there a good reason it is impossible?