Question

How do you implicitly differentiate `3x^2 - 2xy + y^2 = 11`?

Answer 1

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

Explanation:

Start by taking the derivative on both sides of the equation with respect to `x`, bearing in mind that `y` is a function of `x`.
Then solve for `dy/dx`.

`therefore d/dx(3x^2-2xy+y^2)=d/dx11`

`therefore 6x-2xdy/dx-2y+2ydy/dx=0`

`thereforedy/dx=(6x-2y)/(2x-2y)`

`=(2(3x-y))/(2(x-y))`