I got the wrong answer? (implicit differentiation) (not clickbait) (gone wrong)

[ornate estuary]

So I'm doing this problem:
Find by implicit differentiation.
x^2*y^2 + x * sin(y) == 4
(sorry I can't use LaTeX I'm allergic)

I know the next step is to differentiate each side, which (I think) gives us
2x*y^2 + x^2 * + sin(y) + x * cos(y) * == 0

Now I need to isolate

1. Move all the terms that include to the other side
   2x*y^2 + sin(y) == -x^2 * -x * cos(y) *

2. Combine like terms ⚠️(I have a feeling this is where I screwed up)
   2x*y^2 + sin(y) == -x* (x + cos(y))

3. Remove terms from right side
   (2x*y^2 + sin(y)) / -x * (x + cos(y)) ==
   v
   (2x*y^2 + sin(y)) / -x^2 - x * cos(y) ==

The attached image is the answer I was supposed to get, does anyone see my mistake?

[slate minnow]

how do you get from the original equation to the next step?

[ornate estuary]

did I skip a step while taking the derivatives? that part looks right to me

[slate minnow]

shouldn't it be x² * 2y * dy/dx ?

[ornate estuary]

yes

thank you I see it now

is there a command I need to do to close this or

oh wait

thanks @slate minnow!

[slate minnow]

urwelcome