Answer
$$\frac{{dy}}{{dt}} = {9^{2t}}\left( {\ln 81} \right)$$
Work Step by Step
$$\eqalign{
& y = {9^{2t}} \cr
& {\text{Find the derivative of }}y{\text{ with respect to }}t \cr
& \frac{{dy}}{{dt}} = \frac{d}{{dt}}\left[ {{9^{2t}}} \right] \cr
& {\text{Use the general power rule for differentiation }}\cr
&\frac{d}{{dt}}\left[ {{a^u}} \right] = {a^u}\left( {\ln a} \right)\frac{{du}}{{dt}}{\text{ }} \cr
& {\text{for this exercise let }}a = 9{\text{ and }}u = 2t{\text{}}{\text{,}} \cr
& \frac{{dy}}{{dt}} = {9^{2t}}\left( {\ln 9} \right)\frac{d}{{dt}}\left[ {2t} \right] \cr
& {\text{solve the derivative}} \cr
& \frac{{dy}}{{dt}} = {9^{2t}}\left( {\ln 9} \right)\left( 2 \right) \cr
& {\text{simplifying, we get:}} \cr
& \frac{{dy}}{{dt}} = {9^{2t}}\left( {\ln 81} \right) \cr} $$
