Die Kettenregel, angewendet auf

${\displaystyle K^{n}{\stackrel {L}{\longrightarrow }}K^{m}{\stackrel {F}{\longrightarrow }}K,}$

liefert

${\displaystyle {}\left({\frac {\partial {\left(F\circ L\right)}}{\partial X_{1}}},\,\ldots ,\,{\frac {\partial {\left(F\circ L\right)}}{\partial X_{n}}}\right)=\left({\frac {\partial F}{\partial Y_{1}}},\,\ldots ,\,{\frac {\partial F}{\partial Y_{m}}}\right)\circ L\,.}$

Somit ist

${\displaystyle {}{\frac {\partial {\left(F\circ L\right)}}{\partial X_{i}}}\in {\left({\frac {\partial F}{\partial Y_{1}}}\circ L,\ldots ,{\frac {\partial F}{\partial Y_{m}}}\circ L\right)}=L(J_{F})\,}$

und

${\displaystyle {}J_{F\circ L}\subseteq L(J_{F})\,.}$