When taking multiple derivatives of a polynomial, will there ever be an end?
Polynomials are defined as functions that are made entirely of terms like $\displaystyle \displaystyle \begin{align*} a\, x^n \end{align*}$ where $\displaystyle \displaystyle \begin{align*} n \end{align*}$ can only take on nonnegative integer values. What happens to terms that look like this when you differentiate?