Question

How do you differentiate `x^3+y^3=3xy`?

Answer 1

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

Explanation:

differentiate `color(blue)"implicitly with respect to x"`

The `color(blue)"product rule"` has to be used on the right side.

`3x^2+3y^2.dy/dx=3x.dy/dx+3y`

`rArr3y^2dy/dx-3xdy/dx=3y-3x^2`

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

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