analysis Definition Chain Rule Let D⊆Rn an open set, f:D→R a scalar function, and g:R→Rn a vector function with: g(x)=g1(x)g2(x)⋮gn(x) and g(R)⊆D. Let F(x)=(f∘g)(x)=f(g(x)). Then, the derivative F′(x) is given by: F′(x)=∂x∂F=i=1∑n∂gi∂⋅∂x∂gi