Solution
= Solution
Put $q=x^2yz$. The <chain rule> and <product rule> give
$$
\phi_{xx}=(2yz+4x^2y^2z^2)e^q,\qquad
\phi_{yy}=x^4z^2e^q,\qquad
\phi_{zz}=x^4y^2e^q.
$$
Summing these <partial derivatives> gives the <Laplacian>
$$
\boxed{\nabla^2\phi=e^{x^2yz}\left[2yz+4x^2y^2z^2+x^4(y^2+z^2)\right]}.
$$