find the derivative of: (x^2+y^2)^2=x^2-y^2
implicitly ....
2(x^2 + y^2)(2x + 2y dy/dx) = 2x - 2y dy/dx
divide by 2, then expand
2x(x^2 + y^2) + 2y dy/dx(x^2 + y^2) = x - y dy/dx
2y(x^2 + y^2) dy/dx + y dy/dx = x - 2x(x^2 + y^2)
dy/dx = x(1 - 2(x^2 + y^2))/[y(2(x^2+y^2) + 1) ]