Solution
= Solution
For differentiable maps with compatible domains, the multivariable <chain rule> is
$$
\boxed{D(h_2\circ h_1)(x)=Dh_2(h_1(x))\circ Dh_1(x).}
$$
In <Jacobian matrix> notation this is matrix multiplication. In particular, if both maps are <continuously differentiable>, the composition is continuously differentiable. Componentwise,
$$
\partial_j(h_2\circ h_1)_\ell(x)
=\sum_{r=1}^m\partial_r(h_2)_\ell(h_1(x))\,\partial_j(h_1)_r(x).
$$