## Thomas' Calculus 13th Edition

$yx+zx+zy+C$
Consider $f(x,y,z)=yx+zx+g(y,z)$ Also, $\nabla f =F$ and $g_y(y,z)=z$ Then, $g(y,z)=zy+h(z)$ and $h(z)=C$ $f(x,y,z)=yx+zx+zy+h(z)$ Thus, $f(x,y,z)=yx+zx+zy+C$