Es seien ${\displaystyle {}G\subseteq {\mathbb {K} }^{m}}$ und ${\displaystyle {}D\subseteq {\mathbb {K} }^{n}}$ offene Mengen, und ${\displaystyle {}f\colon G\rightarrow {\mathbb {K} }^{n}}$ und ${\displaystyle {}g\colon D\rightarrow {\mathbb {K} }^{k}}$ Abbildungen derart, dass ${\displaystyle {}f(G)\subseteq D}$ gilt. Es sei weiter angenommen, dass ${\displaystyle {}f}$ und ${\displaystyle {}g}$ ${\displaystyle {}\ell }$-fach stetig differenzierbar

${\displaystyle {}g\circ f}$

${\displaystyle {}\ell }$