Answer
See explanation
Work Step by Step
$F(x,y,z)=e^{xy}\textbf{i}-\cos y\textbf{j}+\sin^2 z\textbf{k}$
We determine $divF$:
$divF=ye^{xy}+\sin y+2\sin z\cos z$
W edetermine $curlF$:
$$\begin{aligned}
curlF&= \begin{vmatrix}\textbf{i}&\textbf{j}&\textbf{k}\\\frac{d}{dx}&\frac{d}{dy}& \frac{d}{dz}\\ e^{xy}&-\cos y&\sin^2 z
\end{vmatrix}\\
&=0-0+(-xe^{xy})\textbf{k}\\
&=-xe^{xy}\textbf{k}.
\end{aligned}$$.
