Chapter 15 - Section 15.3 - Path Independence, Conservative Fields, and Potential Functions - Exercises - Page 849: 8

$f(x,y,z)=yx+zx+zy+C$

Since, we have $\nabla f =F$ and $f(x,y,z)=yx+zx+g(y,z)$ ...(1) Here, $g_y(y,z)=z \implies g(y,z)=zy+h(z) $ and $h(z)=0+C$ From equation (1), we have $f(x,y,z)=yx+zx+zy+h(z)=yx+zx+zy+C$ or, $f(x,y,z)=yx+zx+zy+C$