find dy/dx of $\displaystyle \sqrt{xy} = 1 + x^2y$

rewrite

$\displaystyle (xy)^{1/2}-x^2y = 1$

derivative of terms

$\displaystyle \frac{1}{2}(xy)^{-1/2}(xy' + y) - (x^2y' + y2x) = 0$

$\displaystyle \frac{xy'}{2\sqrt{xy}}+\frac{y}{2\sqrt{xy}}-x^2y'-2xy=0$

took more steps but did not get to the answer which is:

$\displaystyle y' = \frac{4xy\sqrt{xy}-y}{x-2x^2\sqrt{xy}}$