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Little confused by something:

if we have u=x+y and v=xy what is the partial derivative w.r.t. u of

y^2=uy-v

I am told it is 2y (dy/du) = u (dy/du) + y

And I can see where these terms come from. What I don't understand is why there is no (dv/du) term, as v and u aren't independent.

Any ideas?