Chain rule: $D(f\circ g)(1,2)=Df(0,0)\,Dg(1,2)$

With $f$ as in Q8, suppose $g:\mathbb{R}^2\to\mathbb{R}^2$ is of class $C^1$ with $g(1,2)=(0,0)$ and $Dg(1,2)=\left(\begin{smallmatrix}1&2\\3&4\end{smallmatrix}\right)$. Then $D(f\circ g)(1,2)=$