Find all points on the curvex^2y^2+ xy = 2
where the slope of the tangent line is -1.
just remember to attach y' = dy/dx when you differentiate a y-term, since you are taking the derivative of y with respect to x. when we are taking the derivative of an x-term, we don't have to attach anything, since we would have dx/dx which cancels to 1. also note that we differentiate xy by the product rule
$\displaystyle x^2 + y^2 + xy = 2$
$\displaystyle \Rightarrow 2x + 2y~y' + y + x~y' = 0$
we want the slope to be -1, so set $\displaystyle y' = -1$ and solve for the resulting function