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