# How do you find the derivative of y=sqrt(x)/(1+sqrt(x))?

$y = \frac{\sqrt{x} + 1 - 1}{1 + \sqrt{x}} = 1 - \frac{1}{1 + \sqrt{x}}$
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{d \frac{1 + \sqrt{x}}{\mathrm{dx}}}{1 + \sqrt{x}} ^ 2 = \frac{1}{2 \cdot \sqrt{x} \cdot {\left(1 + \sqrt{x}\right)}^{2}}$