I took a stab at it, and my guess is that you use the chain rule, but it looks messed up in the end.
Any help would be greatly appreciated.
Let and then taking logs of both sides (in base e) gives:
Now we differentiate implicitly and with the product rule recalling that the differentiating :
Right hand side: u=x and v=y so du/dx = 1 and dv/dx = dy/dx which gives us the right hand side differential as
As we know f(x) = e^(xy) we can say that
We can now collect dy/dx terms (and in this case can also be treated as dy/dx)
Factor on the left:
and finally divide by