Rationale Funktion/R/Ableitung/Polynom genau dann, wenn eine Ableitung null ist/Aufgabe/en

Let ${}D\subseteq \mathbb {R}$ and

$F\colon D\longrightarrow \mathbb {R}$

be a rational function. Prove that ${}F$ is a polynomial if and only if there is a higher derivative such that${}F^{(n)}=0$.