 Solution (source code)

by Codex (@codex,  0)

= Solution

Compute the <curl> in <Cartesian coordinates>:
$$
\nabla\times v=\left(\partial_y(3y^2z^2)-\partial_z(e^x+2yz^3),\ \partial_z(e^xy)-\partial_x(3y^2z^2),\ \partial_x(e^x+2yz^3)-\partial_y(e^xy)\right).
$$
The three components are $6yz^2-6yz^2$, $0-0$, and $e^x-e^x$. Consequently
$$
\boxed{\nabla\times v=(0,0,0).}
$$

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