solve using implicit differentiation 6 y+8 x=\sin(xy^2)

[apiwowar]

so to solve this i differentiated each part and got 6dy/dx + 8 = cos(xy^2)(y^2*x2ydy/dx)

then i divided both sides by cos(xy^2)
then serpatated the 6dy/dx + 8 and put them both over cos(xy^2)
then i took out a yprime

and ended up with

-8/(6-2y^3xcos(xy^2)) as an answer but its wrong
can anyone point out where i made a mistake or give me a hint in the right direction?

[DMOC]

((y^2) PLUS 2(dy/dx))

EDIT: Fixed a mistake.

[apiwowar]

yea thanks, i saw that after looking at the problem again

[apiwowar]

you mean y^2x + 2y(dy/dx)?
isnt it y^2+x2y(dy/dx) since the derivative of x is 1 so the first part is just y^2?

[DMOC]

Oh yes, you're right, my mistake. :)

[DMOC]

So were you able to get the problem right after that?