I was reading that for a function $f:\mathbb{R}^m\rightarrow \mathbb{R}^n$ such that $f(0)=0$ and a function $g:\mathbb{R}^n\rightarrow \mathbb{R}^d$, $J(g\circ f)=J(g)\circ J(f)$ where $J(f)$ denotes the Taylor series of $f$.
I was searching, first by myself and then online a proof of that, but I could'nt find anyone.
Does someone have a source explaining it or any hint I could use?
Thanks!