implicit differentiation?

Question

If 5x^2+5x+xy=2 and y(2)= –14 , find y'(2) by implicit differentiation and please show the steps. thanks!

Answer 1

5(2^2)+5(2)+2y=2
2y=-28
y=-14
10x+5+y+x(dy/dx)=0
x(dy/dx)=-10x-5-y
dy/dx=(-10x-5-y)/x
(-10*2-5-(-14))/2
-11/2
i hope thats right

Answer 2

10xdx + 5dx + xdy + ydx = 0
xdy = -(y + 5 + 10x)dx
dy/dx = -(y + 5 + 10x)/x
y = (2 - 5x - 5x^2)/x
dy/dx = -((2 - 5x - 5x^2)/x + 5 + 10x)/x
y' = dy/dx = -(2 + 5x^2)/x^2
y'(2) = -(2 + 20)/4
y'(2) = -5.5

Answer 3

5x^2+5x+xy=2
dy/dx(5x^2)+dy/dx(5x)+dy/dx(xy)=dy/dy(x2)

10xdy/dx + 5 dy/dx + (x dy/dx + y dx/dx) = 0
(10x +5 )dy/dx + (x dy/dx + y) = 0

(11x + 5)dy/dx = y

dy/dx = y/( 11x +5)
y'(2) = ??????