Which of the following functions f(x,y)f(x, y)f(x,y) satisfies the condition fx=2xy+y2f_x = 2xy + y^2fx=2xy+y2 and fy=x2+2xyf_y = x^2 + 2xyfy=x2+2xy?
x2y+xy2x^2 y + xy^2x2y+xy2
x2y2+xyx^2 y^2 + xyx2y2+xy
x2y+y2x^2 y + y^2x2y+y2
xy2+x2xy^2 + x^2xy2+x2