Chapter 14 - Vector Calculus - 14.5 Divergence and Curl - 14.5 Exercises - Page 1107: 12

$-2xyz$

div $\textbf{F}=\nabla \cdot \textbf{F}=\nabla\cdot\langle x^{2}yz,-xy^{2}z,-xyz^{2}\rangle$ $=\frac{\partial}{\partial x}(x^{2}yz)+\frac{\partial}{\partial y}(-xy^{2}z)+\frac{\partial}{\partial z}(-xyz^{2})$ $=2xyz+-2xyz+-2xyz=-2xyz$