Answer
$$\frac{2}{t}$$
Work Step by Step
$$\eqalign{
& y = \ln \left( {{t^2}} \right) \cr
& {\text{use the logarithmic property }}\ln {a^n} = n\ln a \cr
& y = 2\ln t \cr
& {\text{Find the derivative of }}y{\text{ with respect to }}t \cr
& \frac{{dy}}{{dt}} = \frac{d}{{dt}}\left[ {2\ln t} \right] \cr
& \frac{{dy}}{{dt}} = 2\frac{d}{{dt}}\left[ {\ln t} \right] \cr
& {\text{use the formula }}\frac{d}{{dt}}\ln u = \frac{1}{u}\frac{{du}}{{dt}}{\text{, }}u > 0\cr
& {\text{where }}u{\text{ is any differentiable function of }}t \cr
& \frac{{dy}}{{dt}} = 2\left( {\frac{1}{t}} \right) \cr
& {\text{simplify}} \cr
& \frac{{dy}}{{dt}} = \frac{2}{t} \cr} $$
