#### Answer

$(\ln t)^2+2\ln t$

#### Work Step by Step

$y=t(\ln t)^2$
We differentiate both sides to obtain:
$y^{\prime}=t(\ln t)^2{\prime}+(\ln t)^2(t)^{\prime}$
$y^{\prime}=t(2\ln t)(\ln t)^{\prime}+(\ln t)^2(1)$
$y^{\prime}=t(2\ln t)(\frac{1}{t})+(\ln t)^2$
$y^{\prime}=(\ln t)^2+2\ln t$