If x + y = xy
then dy/dx is?
You can solve the equation for y, but it is simpler to use implicit differentiation (which I presume is what they want here.)
$\displaystyle x + y = xy$ <-- Take the derivative.
$\displaystyle 1 + \frac{dy}{dx} = y + x \cdot \frac{dy}{dx}$
$\displaystyle \frac{dy}{dx} - x \cdot \frac{dy}{dx} = y - 1$
$\displaystyle (1 - x)\frac{dy}{dx} = y - 1$
$\displaystyle \frac{dy}{dx} = \frac{y - 1}{1 - x}$
Now, if you need a form of dy/dx explicitly in terms of y, then
$\displaystyle x + y = xy$
$\displaystyle y - xy = -x$
$\displaystyle y(1 - x) = -x$
$\displaystyle y = -\frac{x}{1 - x}$
You can either just take the derivative of this (not that hard to do) or plug this expression for y into dy/dx and simplify.
-Dan