Answer
$\phi(x,y,z)=xy+z$
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: $f(x,y,z)=y, g(x,y,z) =x$ and $h(x,y,z)=1$
Thus, $\dfrac{\partial f}{\partial y}=1=\dfrac{\partial g}{\partial x}$ and $\dfrac{\partial g}{\partial z}=0=\dfrac{\partial h}{\partial y}$ and $\dfrac{\partial f}{\partial z}=0=\dfrac{\partial h}{\partial x}$
Therefore, a vector field $F$ is Conservative.
Now, potential function $F=\nabla \phi$
So, $\dfrac{\partial \phi}{\partial x}=y \implies \phi(x,y,z)=xy+a(y,z)$
and $\dfrac{\partial \phi}{\partial y}=x=x+\dfrac{\partial a}{\partial y} \implies \dfrac{\partial a}{\partial y}=0 \implies a(y,z)=b(z)$ and $\dfrac{\partial \phi}{\partial z}=1 =b'(z) \implies b(z)=z$
Thus, $\phi(x,y,z)=xy+z$
