If y^3 + y^2 = 7x^2 + 224 and y(2) = 6 then y'(2)= [???]

Answer 1

3y^2 y' + 2y y' = 14x
so,
y' = 14x/(3y^2 + 2y)

You have x=2 and y=6, so plug ='em in.