Answer
div $\textbf{F}=\cos(x+z)-e^{xz}$
curl $\textbf{F}=yxe^{xz}\textbf{i}+\cos(z+x)\textbf{j}-yze^{xz}\textbf{k}$
Work Step by Step
div $\textbf{F}=\nabla\cdot \textbf{F}=\nabla\cdot\langle \sin (x+z),-ye^{xz},0\rangle$
$=\frac{\partial}{\partial x}(\sin (x+z))+\frac{\partial}{\partial y}(-ye^{xz})+\frac{\partial}{\partial z}(0)$
$=\cos (x+z)+(-e^{xz})+0$
$=\cos(x+z)-e^{xz}$
curl $\textbf{F}=\nabla\times\textbf{F}=\nabla\times\langle \sin(x+z),-ye^{xz},0\rangle$
$=(\frac{\partial (0)}{\partial y}-\frac{\partial (-ye^{xz})}{\partial z})\textbf{i}+(\frac{\partial(\sin(x+z))}{\partial z}-\frac{\partial(0)}{\partial x})\textbf{j}+(\frac{\partial(-ye^{xz})}{\partial x}-\frac{\partial(\sin(x+z))}{\partial y})\textbf{k}$
$=(0-(-yxe^{xz}))\textbf{i}+(\cos(z+x)-0)\textbf{j}+(-yze^{xz}-0)\textbf{k}$
$=yxe^{xz}\textbf{i}+\cos(z+x)\textbf{j}-yze^{xz}\textbf{k}$
