Verified answer

2x^2 + 4x + xy = 3

4x * dx + 4dx + xdy + ydx = 0

dx * (4x + 4 + y) = -x * dy

dy / dx = -(4x + 4 + y) / x

x = 3

y = -9

dy/dx = -(4 * 3 + 4 - 9) / 3

dy/dx = -(7) / 3

Diferentiate each and each term, pondering the produt interior the 1st 2 words. 2xy + x^2(dy/dx) -y^3 -x3y^2dy/dx = 0 - 6x^2 now placed dy/dx in information: (dy/dx)(x^2 -3xy^2) = -6x^2 - 2xy + y^3 Then: dy/dx = (-6x^2 -2xy + y^3)/( x^2 -3xy^2) ok