Answer
$y' = \dfrac{1-2xy-3y^3}{x^2+9xy^2}$
Work Step by Step
In order to derivate this function you have to apply implicit differentation method.
First, take the function to it's $f(x) = 0$ form
$x^2y+3xy^3-x-3=0$
Then derivate the whole equation. Rember the put y' every time you derivate y
$2xy+x^2y'+3y^3+9xy^2y'-1=0$
*Note: Here you have to apply the product rule twice
Solve for y' and you have the answer
$y'(x^2+9xy^2) = 1-2xy-3y^3$
$y' = \dfrac{1-2xy-3y^3}{x^2+9xy^2}$
