Find $\omega_2:\Bbb{R}^2→\Bbb{R}$ s.t $\exists$ a $C^\infty$ function $f:\Bbb{R}^2→\Bbb{R}$ for which $df=e^{xy}dx+\omega_2 dy$

Question

I am not sure where to begin on this problem, other than that this problem resembles the structure $df = g\,dx + f\,dy$. This exercise is written in the path independence section of the book, but I am unsure where path independence will play a role here