A curve C has the equation x^3 + 6xy + y^2 = 0. Find dy/dx in terms of x and y.

By differentiating with respect to x, 3x^2+6x(dy/dx)+6y+2y(dy/dx)=0 So, dy/dx(6x+2y)=-3x^2-6y so dy/dx = -(3x^2+6y)/(2(3x+y))