I assume you mean rather than
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