Answer
$$\frac{{dy}}{{dx}} = {3^{ - x}}\ln \left( {\frac{1}{3}} \right)$$
Work Step by Step
$$\eqalign{
& y = {3^{ - x}} \cr
& {\text{Find the derivative of }}y{\text{ with respect to }}x \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {{3^{ - x}}} \right] \cr
& {\text{Use the rule }}\frac{d}{{dx}}\left[ {{a^u}} \right] = {a^u}\ln a\frac{{du}}{{dx}}. {\text{Let }}a = 3{\text{ and }}u = - x{\text{,}} \cr
& \frac{{dy}}{{dx}} = {3^{ - x}}\ln 3\frac{d}{{dx}}\left[ { - x} \right] \cr
& {\text{Solve the derivative and simplify}} \cr
& \frac{{dy}}{{dx}} = {3^{ - x}}\ln 3\left( { - 1} \right) \cr
& \frac{{dy}}{{dx}} = - {3^{ - x}}\ln 3 \cr
& \frac{{dy}}{{dx}} = {3^{ - x}}\ln \left( {\frac{1}{3}} \right) \cr} $$
