Answer
${dy}=\frac{(6\sqrt{x})-y^2}{(2xy-1)}{dx}$
Work Step by Step
We evaluate the function: $xy^2-4\sqrt {(x^3)}-y=0$
on differentiating the above:
$\frac{d(xy^2-4\sqrt {(x^3)}-y)}{dx}=0$
or $2xy\frac{dy}{dx}+y^2-4\times\frac{3}{2}\times\sqrt{x}-\frac{dy}{dx}=0$
or ${(2xy-1)}\frac{dy}{dx}=(6\sqrt{x}-y^2)$
or ${dy}=\frac{(6\sqrt{x})-y^2}{(2xy-1)}{dx}$
The final answer is: ${dy}=\frac{(6\sqrt{x})-y^2}{(2xy-1)}{dx}$
