Answer
$$\frac{{dy}}{{dx}} = \left( {\ln 216} \right){6^{3x - 4}}$$
Work Step by Step
$$\eqalign{
& y = {6^{3x - 4}} \cr
& {\text{Differentiate both sides with respect to }}x \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {{6^{3x - 4}}} \right] \cr
& {\text{Apply }}\frac{d}{{dx}}\left[ {{a^u}} \right] = {a^u}\ln a\frac{{du}}{{dx}} \cr
& \frac{{dy}}{{dx}} = {6^{3x - 4}}\ln \left( 6 \right)\frac{d}{{dx}}\left[ {3x - 4} \right] \cr
& \frac{{dy}}{{dx}} = {6^{3x - 4}}\ln \left( 6 \right)\left( 3 \right) \cr
& {\text{Simplifying}} \cr
& \frac{{dy}}{{dx}} = \left( {3\ln 6} \right){6^{3x - 4}} \cr
& \frac{{dy}}{{dx}} = \left( {\ln 216} \right){6^{3x - 4}} \cr} $$
