For each vector field $\vec{F}(x,y,z)$, compute the curl of $\vec{F}$ and, if possible, find a function $f(x,y,z)$ so that $\vec{F} = \nabla f$. If no such function $f$ exists, enter NONE.

(a) Suppose $\vec{F}(x,y,z) = (4 yz e^{4 xyz} + 3 z^2 \cos(xz^2)) \vec{i} + (4 xz e^{4 xyz})\vec{j} + (4 xy e^{4 xyz} + 6 xz \cos(xz^2))\vec{k}$.
$\mbox{curl}(\vec{F})$ =
$f(x,y,z)$ =

(b) Suppose $\vec{F}(x,y,z) = \displaystyle \frac{\vec{i}}{x} + \frac{\vec{j}}{y} + \frac{\vec{k}}{z}$.
$\mbox{curl}(\vec{F})$ =
$f(x,y,z)$ =

(c) Suppose $\vec{F}(x,y,z) = \langle -2 y, 2 x, 4 z \rangle$.
$\mbox{curl}(\vec{F})$ =
$f(x,y,z)$ =