Answer
$yz\cos x-xz\sin y-xy\sin z$
Work Step by Step
div $\textbf{F}=\nabla \cdot \textbf{F}=\nabla\cdot\langle yz\sin x,xz\cos y,xy\cos z\rangle$
$=\frac{\partial}{\partial x}(yz\sin x)+\frac{\partial}{\partial y}(xz\cos y)+\frac{\partial}{\partial z}(xy\cos z)$
$=yz\cos x+ (-xz\sin y)+(-xy\sin z)$
$=yz\cos x-xz\sin y-xy\sin z$
