Implicit function theorem application

Question

I'm supposed to find supposed to find $ \frac{dy}{dx}$ where the function is defined implicitly as $x^2-3xy^3+x^2y^2+7=0$, by setting up $F(x,y)=x^2-3xy^3+x^2y^2+7=0$ , via direct application of formula we get $\frac{dy}{dx}= -\frac{F_x}{F_y}$ . But I get the feeling that this is not entirely accurate, can somebody walk me through the process here ?

Answer 1

we have $F(x,y(x))=0$ and by differentiating with respect to $x$ we get $F_x+F_yy'=0$ thus we have $$y'=-\frac{F_x}{F_y}$$ if $F_y\ne 0$.