Question

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

Answer 1

Given -

`-y^2=xy^3-x^4y`

`-2ydy/dx=[x.3ydy/dx+y^3 . 1]-[x^4dy/dx+y.4x^3]`

`-2ydy/dx=3xydy/dx+y^3-x^4+4x^3y`
`-2ydy/dx-3xydy/dx=y^3-x^4+4x^3y`
`-(2y+3xy)dy/dx=y^3-x^4+4x^3y`
`-y(2+3x)dy/dx=y^3-x^4+4x^3y`
`dy/dx=(y^3_x^4+4x^3y)/(-y(2+3x)`