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

$-(e^{-x+y}+ e^{-y+z}+e^{-z+x})$

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