#### Answer

$yx+zx+zy+C$

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

Published by
Pearson

ISBN 10:
0-32187-896-5

ISBN 13:
978-0-32187-896-0

$yx+zx+zy+C$

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