Answer
The function $f$ is not a conservative vector field.
Work Step by Step
Here, we have $f(x,y)=x^2 y$ and $g(x,y)=y \ln x$
In order to find the function as a conservative vector field, we must have $\dfrac{\partial f}{\partial y}=\dfrac{\partial g}{\partial x}$
Thus, $\dfrac{\partial f}{\partial y}=\dfrac{x}{y}$ and $\dfrac{\partial g}{\partial x}=\dfrac{y}{x}$
So, $\dfrac{\partial f}{\partial y} \ne \dfrac{\partial g}{\partial x}$
This means that the function $f$ is not a conservative vector field.
