Computing scalar derivative by chain rule with matrix intermediary

Question

Consider a function function $h(x) = f(g(x))$ where $g(x): \mathbb{R} \to \mathbb{R}^{m \times n}$ and $f(A): \mathbb{R}^{m \times n} \to \mathbb{R}$.

How can I compute $\frac{d[h(x)]}{dx}$ in terms of the Jacobians of $g$ and $f$?