Question

How do you implicitly differentiate `-y= 4x^3y^2+2x^2y^3`?

Answer 1

`dy/dx=(6xy + 2y^2)/(4x^2 + 3xy)`

Explanation:

`d/dx= 12x^2y^2 + 4xy^3`

`d/dy=8x^3y + 6x^2y^2`

note that
`d/dy*dy/dx=d/dx`
leading to
`(8x^3y + 6x^2y^2)*dy/dx -12x^2y^2 +4xy^3=0`

`dy/dx=(12x^2y^2 + 4xy^3)/(8x^3y + 6x^2y^2)`

`dy/dx=(6xy + 2y^2)/(4x^2 + 3xy)`