Consider the following differential equation.

$\frac{dy}{dx}=\sqrt[\phantom{2}]{xy}$

Let $f(x,y)=\sqrt[\phantom{2}]{xy}.$ Find the derivative $off.$

$\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}}=$

Determine a region $of$ the $xy{x}_0,y_{0}xy-$plane.

There $is$ a unique solution $in$ the region $xy.$

There $is$ a unique solution $in$ any rectangular region where $x>0$ and $y>0orx<mn>0</mn>$ and

There $is$ a unique solution $in$ any rectangular region where $x>0$ and $y>0orx>0$ and

There $is$ a unique solution $in$ any rectangular region where $x<mn>0</mn>$ and $y>0.$