If `x^3+y^3=3a x y` , find `(dy)/(dx)`

Answer

`(ay-x^(2))/(y^(2)-ax)`

Explanation

Given `x^(3)+y^(3)-3axy = 0`. From
`(dy)/(dx)=-("differentiating f w.r.t. x keeping y as consant")/("differentiating f w.r.t. y keeping x as constant")`
`=-(3x^(2)-3ay)/(3y^(2)-3ax)=(ay-x^(2))/(y^(2)-ax)`