Let URkU\subseteq\mathbb R^k and VRmV\subseteq\mathbb R^m be . If f:UVf:U\to V is at aUa\in U and g:VRpg:V\to\mathbb R^p is differentiable at f(a)f(a), then the gfg\circ f is differentiable at aa, and

D(gf)(a)=Dg(f(a))Df(a).D(g\circ f)(a)=Dg(f(a))\circ Df(a).

In terms of , this is

Jgf(a)=Jg(f(a))Jf(a).J_{g\circ f}(a)=J_g(f(a))\,J_f(a).