# implicit differentiation

• Dec 3rd 2007, 05:39 PM
singh1030
implicit differentiation
Find all points on the curve
x^2
y^2+ xy = 2
where the slope of the tangent line is -1.

• Dec 3rd 2007, 06:03 PM
Jhevon
Quote:

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 \$\displaystyle x^2 + y^2 + xy = 2\$ ??
• Dec 3rd 2007, 06:05 PM
singh1030
yea i did sorry
• Dec 3rd 2007, 06:12 PM
Jhevon
Quote:

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

\$\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