How would I solve for $y'$ using implicit differentiation?
$x^2 + 2xy -y^2 + x = 2$
How would I solve for $y'$ using implicit differentiation?
$x^2 + 2xy -y^2 + x = 2$
Product rule, chain rule and power rule will get you the expression in terms of $x,y,$ and $y'$. Gather all your $y'$ terms on one side, factor it out, then divide by the other factor to solve for $y'$.
Differentiate both sides with respect to $x$, keeping the chain rule in mind, to get $2x+2y+2xy'-2yy'+1=0$
Now isolate $y'$ and we're done: $y'(2x-2y)=-2x-2y-1$. Therefore, $y'=?$