\[ \newcommand{\d}{\mathrm{d}} \newcommand{\e}{\mathrm{e}} \newcommand{\i}{\mathrm{i}} \]

Let \(f\colon \mathbb{R}^m\to \mathbb{R}^k\) and \(f\colon \mathbb{R}^n\to \mathbb{R}^m\) differentiable. Then for \(a\in \mathbb{R}^n\) we have

\begin{equation*} D_a(f\circ g)=D_{g(a)}f\circ D_ag \end{equation*}

or in short

\begin{equation*} D(f\circ g)=Df\circ Dg. \end{equation*}