# Math Help - implicit differentiation

1. ## implicit differentiation

Find all points on the curve
x^2
y^2+ xy = 2
where the slope of the tangent line is -1.

2. Originally Posted by singh1030
Find all points on the curve
x^2
y^2+ xy = 2
where the slope of the tangent line is -1.
do you mean $x^2 + y^2 + xy = 2$ ??

3. yea i did sorry

4. Originally Posted by singh1030
yea i did sorry
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

$x^2 + y^2 + xy = 2$

$\Rightarrow 2x + 2y~y' + y + x~y' = 0$

we want the slope to be -1, so set $y' = -1$ and solve for the resulting function