The curve C has equation x^2 + 2xy + 3y^2 = 4. Find dy/dx.

Here, we have to use implicit differentiation, along with the product rule. Remember that the product rule is (vu)' = vu'+uv'. Moving through the equation we have: x^2+2xy+3y^2 = 4 ==> 2x +2y + 2x*(dy/dx) + 6y*(dy/dx) = 0, remembering the rules of implicit differentiation. Factorising out dy/dx = -(2x+2y)/(2x+6y).