I don't know where you got that " " from. "Leibniz formula" says

Here, so its derivative is 0, and so its derivative is 1. . That does not depend upon x so [tex]\frac{\partial f(x, t)}{\partial x}= 0[tex]

That is the derivative of the integral is simply f(x,x)= 2xy(x).

As for the second, you differentiate with respect to x and yindependently, that is, you take the partial derivatives. There should be no "dy/dx" in the formulas.