>In single variable calculus, the chain rule can be written as ddxf(g(x))=f′(g(x))g′(x). In the multivariable case, for a function f:Rk→R, we write ddxf(g(x))=∑ki=1ddxgi(x)Dif(g(x)) where Di is the partial derivative of f with respect to its ith argument. This can be simplified by employing the following notation, which uses a dot product: ddxf(g(x))=∇f⋅g′(x).
What does gi() stand for? My understanding that g maps g:Rm→Rk and gi indicates i-th element of a vector that g produces.
In this paragraph:
>In single variable calculus, the chain rule can be written as ddxf(g(x))=f′(g(x))g′(x). In the multivariable case, for a function f:Rk→R, we write ddxf(g(x))=∑ki=1ddxgi(x)Dif(g(x)) where Di is the partial derivative of f with respect to its ith argument. This can be simplified by employing the following notation, which uses a dot product: ddxf(g(x))=∇f⋅g′(x).
What does gi() stand for?
My understanding that g maps g:Rm→Rk and gi indicates i-th element of a vector that g produces.
Is that the right way to think about it?