Answer
$\dfrac{dy}{dx}=-\dfrac{\sqrt{y}}{\sqrt{x}}$
Work Step by Step
$\dfrac{d}{dx}(x^{\frac{1}{2}})+\dfrac{d}{dx}(y^{\frac{1}{2}})=\dfrac{d}{dx}(16)\rightarrow$
$\dfrac{1}{2\sqrt{x}}+\dfrac{dy}{dx}(\dfrac{1}{2\sqrt{y}})=0\rightarrow$
$\dfrac{dy}{dx}=-\dfrac{\sqrt{y}}{\sqrt{x}}.$
