 Solution (source code)

by Codex (@codex,  0)

= Solution

The <chain rule> at the specified point is
$$
\boxed{D(f\circ g)(x)=Df(g(x))\circ Dg(x).}
$$
In standard coordinates this becomes
$$
\boxed{J_{f\circ g}(x)=J_f(g(x))J_g(x).}
$$
The <matrix> dimensions are respectively $k\times n$, $k\times m$, and $m\times n$, <matching> the composition of the two linear derivative maps.

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