Question

How do you find the derivative of `x^3+xy^2=y^3+yx^2`?

Answer 1

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

Explanation:

Differentiating both sides of the given equation w.r.t x, it would result in

`3x^2+ x 2ydy/dx +y^2 = 3y^2 dy/dx +y (2x) +x^2 dy/dx`

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

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