Answer
$\frac{1}{2t\sqrt{1+\ln t}}$
Work Step by Step
$\frac{d}{dt}\sqrt{1+\ln t}$
$\frac{d}{dt}(1+\ln t)^\frac{1}{2}$
$=\frac{1}{2}(1+\ln t)^{-\frac{1}{2}}\frac{d}{dt}(1+\ln t)$
$=\frac{1}{2\sqrt{1+\ln t}}*\frac{1}{t}$
$=\frac{1}{2t\sqrt{1+\ln t}}$
