0
$\begingroup$

How would I solve for $y'$ using implicit differentiation?

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

2 Answers 2

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 $y'$.

  • 0
    @user44816: You're very close! You want to gather all the $y'$ terms on one side, though. I see that you gathered all the terms with a $y$ **or** a $y'$ on one side, but we want **just** the $y'$ terms. One of the terms you've got on the left-hand side still needs to be moved to the other side--in particular, the one without a $y'$ in it.2012-11-12
1

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, $y'=?$