Answer
$\phi(x,y,z)=xy+yz+xz$
Work Step by Step
For a vector field to be Conservative, $\dfrac{\partial f}{\partial y}=\dfrac{\partial g}{\partial x}$ and $\dfrac{\partial g}{\partial z}=\dfrac{\partial h}{\partial y}$ and $\dfrac{\partial f}{\partial z}=\dfrac{\partial h}{\partial x}$
We have: $f(x,y,z)=y+z, g(x,y,z) =x+z$ and $h(x,y,z)=x+y$
Thus, $\dfrac{\partial f}{\partial y}=1=\dfrac{\partial g}{\partial x}$ and $\dfrac{\partial g}{\partial z}=1=\dfrac{\partial h}{\partial y}$ and $\dfrac{\partial f}{\partial z}=1=\dfrac{\partial h}{\partial x}$
Therefore, a vector field $F$ is Conservative.
Now, potential function $F=\nabla \phi$
So, $\dfrac{\partial \phi}{\partial x}=y+z \implies \phi(x,y,z)=xy+xz+a(y,z)$
and $\dfrac{\partial \phi}{\partial y}=x+z=x+\dfrac{\partial a}{\partial y} \implies \dfrac{\partial a}{\partial y}=z \implies a(y,z)=yz+b(z)$ and $\dfrac{\partial \phi}{\partial z}=x+y =x+b'(z) \implies b(z)=yz$
Thus, $\phi(x,y,z)=xy+yz+xz$
