$\displaystyle (x+y)^3 = x^3 + y^3$ at the point (-1,1). We need to find y' ... what do?
Here's what I did, please tell me where I went wrong.
3(x+y)^2 (1+y') = 3x^2 + 3y^2 y'
How do I proceed?
$\displaystyle (x^2 + 2xy + y^2)(1 + y') = x^2 + y^2 y'$
$\displaystyle x^2 + 2xy + y^2 + x^2 y' + 2xy y' + y^2 y' = x^2 + y^2 y'$
$\displaystyle y' (x^2 + 2xy) = -2xy - y^2$
$\displaystyle y' = (-2xy - y^2)/(x^2 + 2xy)$
This should be correct.
I apologize for my mistake, if it serves as an excuse, I was solving it in my head because i couldn't find paper.