From what we did in class i have that the function is conservative if $\frac{δ P}{δ Y}=\frac{δ Q}{δ X}$.
So I found $\frac{δ P}{δ Y}=e^x\sin(y)$ and then $\frac{δ Q}{δ X}=\sin(y)e^x$.
But the book answer says that it's not conservative. I put them into symbolab to make sure I wasn't somehow doing something stupid with the derivatives and got the same back. Is my understanding of how to check for it being conservative incorrect?