MHB Can Implicit Differentiation Be Done by Separation of Variables?

[karush]

$\tiny{s8.2.6.2}$
Find y' of $2x^2+x+xy=1
$\begin{array}{lll}
\textit{separate variables}
&xy=2x^2+x+1 \implies y=\dfrac{2x^2+x+1}{x}\implies 2x+1+x^{-1}
&(1)\\ \\
\textit{differencate both sides}
&y'=2-\dfrac{1}{x^2}
&(2)
\end{array}

ok it seems we can do any implicit differentiation by separation or not?
I think I got the right answer hopefully

 

[skeeter]

watch those signs ...

$y=\dfrac{1-x-2x^2}{x} = \dfrac{1}{x} - 1 - 2x$

$y’ = -\dfrac{1}{x^2} - 2$

 

[karush]

watch those signs ...

$y=\dfrac{1-x-2x^2}{x} = \dfrac{1}{x} - 1 - 2x$

$y’ = -\dfrac{1}{x^2} - 2$

yikes... ok