Work Step by Step
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, $f(x,y,z)=yx+zx+zy+C$
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.