$\displaystyle curl\ \vec{F}=\left[\begin{array}{ ccc} i & j & k \\ \frac{\partial{}}{\partial{}x} & \frac{\partial{}}{\partial{}y} & \frac{\partial{}}{\partial{}z} \\ xye^{2z} & xy^2\cos z & x^2\cos xy \end{array}\right] \\[2ex] $

$\displaystyle =i\left[x^2\frac{\partial{}}{\partial{}y}\cos xy-xy^2\frac{\partial{}}{\partial{}z}\cos z\right]-j\left[\frac{\partial{}}{\partial{}x}x^2\cos xy-xy\frac{\partial{}}{\partial{}z}e^{2z}\right]+k\left[y^2\cos z\frac{\partial{}}{\partial{}x}x-xe^{2z}\frac{\partial{}}{\partial{}y}y\right] \\[2ex] \displaystyle =i\left[x^2\left(-\sin y\right)x+xy^2\sin z\right]-j\left[-2xy\sin x-xye^{2z}\bullet{}2\right]+k\left[y^2\cos z-xe^{2z}\right] \\[2ex] \displaystyle =i\left[-x^3\sin y+xy^2\sin z\right]-j\left[-2xy\sin x-2xye^{2z}\right]+k\left[y^2\cos z-xe^{2z}\right] \\[2ex] $

$\displaystyle \ Now\ div\ \vec{F}=\nabla{}\bullet{}\vec{F} \\[2ex] \displaystyle =i\frac{\partial{}}{\partial{}x}\left(xye^{2z}\right)+j\frac{\partial{}}{\partial{}y}\left(xy^2\cos z\right)+k\frac{\partial{}}{\partial{}z}\left(x^2\cos xy\right) \\[2ex] \displaystyle =i(ye^{2z})+j\left(2xy\cos z\right)+k(x^2\cos xy) \\[2ex]$