Answer
$$\frac{3}{{2t}}$$
Work Step by Step
$$\eqalign{
& y = \ln \left( {{t^{3/2}}} \right) \cr
& {\text{use the logarithmic property }}\ln {a^n} = n\ln a \cr
& y = \frac{3}{2}\ln t \cr
& {\text{Find the derivative of }}y{\text{ with respect to }}t \cr
& \frac{{dy}}{{dt}} = \frac{d}{{dt}}\left[ {\frac{3}{2}\ln t} \right] \cr
& \frac{{dy}}{{dt}} = \frac{3}{2}\frac{d}{{dt}}\left[ {\ln t} \right] \cr
& {\text{use the formula }}\frac{d}{{dt}}\ln u = \frac{1}{u}\frac{{du}}{{dt}}{\text{, }}u > 0\cr
& {\text{ where }}u{\text{ is any differentiable function of }}t \cr
& \frac{{dy}}{{dt}} = \frac{3}{2}\left( {\frac{1}{t}} \right) \cr
& {\text{simplify}} \cr
& \frac{{dy}}{{dt}} = \frac{3}{{2t}} \cr} $$
