dy/dx when $\displaystyle -xy^2 + 10x^2y = -x + 2$
i got
(10x^2 - 2yx + 10xy + 1) / y^2 = dy/dx
can some one please check if this is right
ok, i'll post. see if you can spot a mistake, if any. i'm kind of tired and too lazy to check through it myself, it will be good practice for you
$\displaystyle -xy^2 + 10x^2 y = -x + 2$
differentiating implicitly we get
$\displaystyle -y^2 - 2xy~\frac {dy}{dx} + 20xy + 10x^2~\frac {dy}{dx} = -1$
$\displaystyle \Rightarrow \frac {dy}{dx} \left( 10x^2 - 2xy \right) = y^2 - 20xy - 1$
$\displaystyle \Rightarrow \frac {dy}{dx} = \frac {y^2 - 20xy - 1}{10x^2 - 2xy}$
everything good?