Answer
$f'(x)=\frac{2}{(x+2)^2}$
$f''(x)=\frac{-4}{(x+2)^3}$
Work Step by Step
$f(x)=\frac{x}{x+2}$
Using Quotient Rule, where $(\frac{f}{g})'=\frac{f'g-fg'}{g^2}$
$f'(x)=\frac{(1)(x+2)-(x)(1)}{(x+2)^2}=\frac{2}{(x+2)^2}$
Using Quotient Rule and Chain Rule:
$f''(x)=\frac{(0)(x+2)^2-2(2)(1)(x+2)}{(x+2)^4}=\frac{-4}{(x+2)^3}$
