Question

How do you use implicit differentiation to find dy/dx given `x^3+y^3=6xy-1`?

Answer 1

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

Explanation:

`x^3+y^3=6xy-1`

`3x^2+3y^2 dy/dx=6y+6x dy/dx`

`3y^2 dy/dx-6x dy/dx=6y-3x^2`

`dy/dx (3y^2-6x)=6y-3x^2`

`dy/dx=(6y-3x^2)/(3y^2-6x)`

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