Solution
= Solution
The derivative of the curve is
$$
\boxed{Dg(t)h=h\begin{pmatrix}\cos t\\-\sin t\end{pmatrix}.}
$$
Its image lies on the unit circle, so $f(g(t))=1/2$ and $\boxed{D(f\circ g)(t)=0}$. Meanwhile
$$
J_f(g(t))=\begin{pmatrix}-\sin t/2&-\cos t/2\end{pmatrix},
$$
and multiplication by $J_g(t)$ gives $-\sin t\cos t/2+\cos t\sin t/2=0$. This verifies the <chain rule> explicitly.