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