posted by DJ .
Use implicit differentiation to find the slope of the tangent line to the curve
2(x^2) + 2xy + 2(y^3)= -18
What's the problem? If you understand implicit differentiation, it's just crank away:
4x + 2y + 2xy' + 6y^2 y' = 0
y'(2x + 6y^2) = -4x - 2y
y' = -2(2x+y)/2(x+3y^2) = -(2x+y)/(x+3y^2)