Answer
$\displaystyle \frac{1-2\ln t}{t^{3}}$
Work Step by Step
Quotient rule, with $\displaystyle \frac{d}{dt}\ln t=\frac{1}{t}$
$g^{\prime}(t)=\displaystyle \frac{(\frac{1}{t})\cdot t^{2}-\ln t\cdot(2t)}{(t^{2})^{2}}=\frac{t-2t\ln t}{t^{4}}=\frac{t(1-2\ln t)}{t^{4}}=\frac{(1-2\ln t)}{t^{3}}$
