I'm doing this problem:
Let: $g:\mathbb{R}^{2} \rightarrow \mathbb{R}^2$ and $f:\mathbb{R}^{2} \rightarrow \mathbb{R}^2$ be a differentiable function such that:
$g(0,0)=(1, 2); \ \ g(1,2)=(3,5); \ \ f(0,0)=(3,5); \ \ f(4,1)=(1,2)$
$Dg(0,0) = \left[ {\begin{array}{cc} 1 & 0 \\ -1 & 4 \end{array}} \right]; \ \ \ Dg(1,2)= \left[{\begin{array}{cc} 2 & 3 \\ 5 & 7 \end{array}}\right]; \ \ \ Df(3, 5) = \left[{\begin{array}{cc} 1 & 1 \\ 3 & 5 \end{array}}\right]; \ \ \ Df = \left[{\begin{array}{cc} -1 & 2 \\ 1 & 3 \end{array}}\right]$
Calculate: $D(f \ o \ g)(1, 2)$
I think the solution is:
$D(f(g))(1,2) = \left[{\begin{array}{cc} 2 & 3 \\ 5 & 7 \end{array}}\right]\left[{\begin{array}{cc} 1 & 1 \\ 3 & 5 \end{array}}\right]$
Because I used the chain rule, then: $Dg*Df$, but I'm not sure about that, I mistake?