Take the derivative of x^2 to get 2x.
Take the derivative of -2xy to get -2y +-2x[tex] \frac{dy}{dx} [/tex] (Everytime you take the derivative of y, you write [tex] \frac{dy}{dx} [/tex].
Take the derivative of -3y^2 to get -6y[tex] \frac{dy}{dx} [/tex].
Get the terms with [tex] \frac{dy}{dx} [/tex] on one side to get:
-2x[tex] \frac{dy}{dx} [/tex] - 6y[tex] \frac{dy}{dx} [/tex] = 2x - 2y
Take out the common factor of [tex] \frac{dy}{dx} [/tex] to get:
[tex] \frac{dy}{dx} [/tex][-2x - 6y] = 2x - 2y
Divide by -2x - 6y to get:
[tex] \frac{dy}{dx} [/tex] = [tex] \frac{2x - 2y}{-2x - 6y} [/tex]
