Answer
$y'=\dfrac{\dfrac{2+x}{2\sqrt{x}}+\sqrt{x}}{4+4x+x^2}$
Work Step by Step
Identify a and b for apply quotient rule
$a=\sqrt(x)$
$a'=\dfrac{1}{2\sqrt{x}}$
$b=2+x$
$b'=1$
Substitute in the formula $(\dfrac{a}{b})'=\dfrac{a'b-ab'}{b^2}$
$y'=\dfrac{(\dfrac{1}{2\sqrt{x}})(2+x)+(\sqrt{x})(1)}{(2+x)^2}$
$y'=\dfrac{\dfrac{2+x}{2\sqrt{x}}+\sqrt{x}}{4+4x+x^2}$
