Implicit differentiation of x^2y+xy^2=sin(y): find dy/dx

[Calculusishard]

Hello, I'm trying to study for an exam and I would really appreciate some help with this problem.

x^2y+xy^2=sin(y)
find dy/dx using implicit differentiation

I started by taking the derivative of both sides using chain and product rule as follows:

2xy+x^2(dy/dx)+y^2+y(dy/dx)=cos(y)sin(dy/dx)

I know from here I should try to get dy/dx by itself and solve, but I'm not even sure if I did the first part correctly. Any help is much appreciated!!

 

[Deleted member 4993]

Hello, I'm trying to study for an exam and I would really appreciate some help with this problem.

x^2y+xy^2=sin(y)
find dy/dx using implicit differentiation

I started by taking the derivative of both sides using chain and product rule as follows:

2xy + x^2 *(dy/dx) + y^2 + (x) * 2* y * (dy/dx)=cos(y) (dy/dx) .... almost make the necessary corrections.

I know from here I should try to get dy/dx by itself and solve, but I'm not even sure if I did the first part correctly. Any help is much appreciated!!

.