#### Answer

$s'(t) = \frac{1}{(2t+1)^{2}}$

#### Work Step by Step

$s(t) = \frac{t}{2t+1}$
Using the derivative definition:
$s'(t) = \lim\limits_{h \to 0}\frac{\frac{t+h}{2(t+h)+1} - \frac{t}{2t+1}}{h}$
$s'(t) = \lim\limits_{h \to 0}\frac{h}{h(2t+1)^{2}}$
$s'(t) = \frac{1}{(2t+1)^{2}}$