Answer
$\frac{dy}{dx}=(-\frac{\sqrt{x}}{2\sqrt{x+1}})(\frac{1}{({x})^2})$
Work Step by Step
$y=\sqrt{(\frac{{x^2+x}}{{x}^2})}=\sqrt{(\frac{{x+1}}{{x}})}$
on applying differentiation:
$\frac{dy}{dx}=\frac{1}{2\sqrt{(\frac{{x+1}}{{x}})}}\frac{d}{dx}{(\frac{{x+1}}{{x}})}$
$\frac{dy}{dx}=\frac{1}{2\sqrt{(\frac{{x+1}}{{x}})}}(\frac{-(1+{x})\frac{d}{dx}({x})+{x}\frac{d}{dx}{(1+{x})}}{({x})^2})$
$\frac{dy}{dx}=(-\frac{\sqrt{x}}{2\sqrt{x+1}})(\frac{1}{({x})^2})$
