d/dx (x/y) = (y+xy')/y^2 [By quotient rule]
d/dx (x^2/y^2)
= d/dx ((x/y)^2)
= 2(x/y).d/dx (x/y) [By chain rule]
= 2x/y.(y+xy')/y^2
= 2x(y+xy')/y^3
Might be a problem in the solution.
Just treat it as a normal derivative but when differentiating y wrt x, let d/dx (y)=dy/dx=y'