How do i explicitly differentiate this? 16x^2 + 9y^2 = 144

so i got it to this point: sqrt((-16x^2+144)/9)=y and that is looking pretty nasty when i derive it and simplify it and i'm not getting the same thing as when i implicitly differentiate it

9y^2 = 144 - 16x^2
y^2 = (144 - 16x^2) / 9
y = (1/3) * (144 - 16x^2)^(1/2)
dy/dx = (1/3) * (1/2) * (-32x) / (144 - 16x^2)^(1/2)
dy/dx = (-16x / 3) / sqrt(144 - 16x^2)
dy/dx = -16x / (3 * sqrt(144 - 16x^2))

Now, let's differentiate implicitly:

16x^2 + 9y^2 = 144
32x * dx + 18y * dy = 0
16x * dx + 9y * dy = 0
9y * dy = -16x * dx
dy / dx = -16x / (9y)

Remember that y = (1/3) * sqrt(144 - 16x^2)

dy/dx = -16x / (9 * (1/3) * sqrt(144 - 16x^2))
dy/dx = -16x / (3 * sqrt(144 - 16x^2))

Same answer, huh?