You should differentiate this identity.


To facilitate it, differentiate each addend separately.


    (x^2*y^2)' = 2x*y^2 + 2x^2*y*y' 

    (xy)' = y + xy'

    x' = 1

    1' = 0.


Then combine these derivatives in one formula


    2x*y^2 + 2x^2*y*y' - y - xy' + 1 = 0


Keep the terms with y' on the left side; move the rest of the terms to the right side


    2x^2*y*y' - xy' = 2x*y^2 + y - 1


In the left side, factor out the common factor y'


    (2x^2*y - x)*y' = 2x*y^2 + y - 1


Express y', dividing both sides by  (2x^2*y - x)


    y' = .


Thus the formula is just ready.

To get the value,  substitute the values  x= 1, y= 1 into the formula.  You will get then


    y' =  =  =  = 2.    ANSWER


ANSWER.  y' = 2.