find slope of the line at 3x^2+2xy+6y^2-3x-8y=0 at (1,1) I'm so lost, this review is killing me *leafs through notebook*

also, the integral of tan^2x+sinx , my brain is melting before finals. Help would be much appreciated. :)

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- May 19th 2008, 04:11 PM333arizonaIntegral and a slope problem
find slope of the line at 3x^2+2xy+6y^2-3x-8y=0 at (1,1) I'm so lost, this review is killing me *leafs through notebook*

also, the integral of tan^2x+sinx , my brain is melting before finals. Help would be much appreciated. :) - May 19th 2008, 04:21 PMMathstud28
- May 19th 2008, 04:32 PMMathstud28
$\displaystyle 3x^2+2xy+6y^2-3x-8y=0$

differntiating implicity we get

$\displaystyle 6x+2[xy'+y]+12y\cdot{y'}-3-8y'=0$

Substituting $\displaystyle x=1$ and $\displaystyle y=1$

we get $\displaystyle 6(1)+2[y'+1]+12\cdot{y'}-3-8y'=0\Rightarrow{5+6y'=0}\Rightarrow{y'=\frac{-5}{6}}$