Answer
$$f'\left( t \right) = 1.3\left( {{2^t}\ln 2} \right)$$
Work Step by Step
$$\eqalign{
& f\left( t \right) = 1.3\left( {{2^t}} \right) \cr
& {\text{Calculate the derivative of the function}} \cr
& f'\left( t \right) = \frac{d}{{dt}}\left( {1.3\left( {{2^t}} \right)} \right) \cr
& f'\left( t \right) = 1.3\frac{d}{{dt}}\left( {{2^t}} \right) \cr
& {\text{Compute derivatives}}{\text{, use the rule }}\frac{d}{{dt}}\left( {{a^t}} \right) = {a^t}\ln a \cr
& f'\left( t \right) = 1.3\left( {{2^t}\ln 2} \right) \cr} $$