Answer
$\frac{dy}{dx}=\frac{-y}{x}$
Work Step by Step
Rewrite the equation: $(xy)^{1/2}=1$
Take the derivative of the equation on each side separately. Apply chain rule when differentiating the "y" variables since we are differentiating with respect to x:
$\frac{1}{2}(xy)^{-1/2}\times(x\frac{dy}{dx}+y)=0$
Move all terms with dy/dx to one side of the equation, and isolate dy/dx:
$x\frac{dy}{dx}+y=0$
$\frac{dy}{dx}=\frac{-y}{x}$
