Question

What is the implicit derivative of `1= xy-(xy-1)^2+2y`?

Answer 1

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

Explanation:

Differentiate 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(1)=d/dx(xy-(xy-1)^2+2y)`

`therefore0=xdy/dx+y-2(xy-1)*(xdy/x+y)+2dy/dx`

`therefore 0=xdy/dx+y-2x^2ydy/dx-2xy^2+2xdy/dx+2y+2dy/dx`

`thereforedy/dx=(2xy^2-3y)/(3x-2x^2y+2)`