Question

How do you implicitly differentiate `-1=5y^3x-2xy+3x^2y`?

Answer 1

`dy/dx= -(5y^3 -2y +6xy)/(15xy^2 -2x +3x^3)`

Explanation:

Differentiate both sides terms wise
`(d/dx -1)= 5d/dx y^3 x -2 d/dx xy +3 d/dx x^2y`

`0=5(y^3 +x 3y^2 dy/dx)-2(y +x dy/dx) +3(2xy +x^2 dy/dx)`

`0=(5y^3 -2y +6xy)+(15xy^2 -2x +3x^3 )dy/dx`

`dy/dx= -(5y^3 -2y +6xy)/(15xy^2 -2x +3x^3)`