Question

How do you find `(dy)/(dx)` given `y^3+x^3=3xy`?

Answer 1

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

Explanation:

`y^3+x^3=3xy`

`3y^2dy/dx + 3x^2 = 3(xdy/dx+y*1)`
(Inplicit differentiation, Power rule and Product rule)

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

Multiply through by `(-1/3) ->`
`(x-y^2)dy/dx= (x^2-y)`

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