Answer
a) $(\arctan (\dfrac{x}{z})-e^{xy} \cos z)i-\dfrac{yz}{z^2+x^2}j+ye^{xy} \sin z k$
b) $xe^{xy} \sin z-\dfrac{xy}{z^2+x^2}$
Work Step by Step
a) $curl F=(\arctan (x/z)-e^{xy} \cos z)i-(yz/1+x^2)-0)j+(xe^{xy} \sin z-0) k$
or, $=(\arctan (\dfrac{x}{z})-e^{xy} \cos z)i-\dfrac{yz}{z^2+x^2}j+ye^{xy} \sin z k$
b) $div F=\dfrac{\partial a}{\partial x}+\dfrac{\partial b}{\partial y}+\dfrac{\partial c}{\partial z}$
$div F=\dfrac{\partial (0)}{\partial x}+\dfrac{\partial (e^{xy} \sin z)}{\partial y}+\dfrac{\partial (y \arctan (xz^{-1})}{\partial z}$
or, $=xe^{xy} \sin z-\dfrac{xy}{z^2+x^2}$
