Solution
= Solution
{c}
For a differentiable map $f:\Omega\subset\mathbb R^n\to\mathbb R^k$, the <Jacobian matrix> represents its derivative and has entries $(Df)_{ij}=\partial f_i/\partial x_j$. Differentiating the two components gives
$$
\boxed{Df(x,y)=
\begin{pmatrix}
e^x\sin y&e^x\cos y\\
-e^{-y}\sin x&-e^{-y}\cos x
\end{pmatrix}.}
$$