Answer
$F'\left( t \right) = 3{t^2}$
Work Step by Step
$$\eqalign{
& F\left( t \right) = {t^3} + {e^3} \cr
& {\text{Differentiate the function}} \cr
& F'\left( t \right) = \frac{d}{{dt}}\left[ {{t^3} + {e^3}} \right] \cr
& {\text{Use the constant multiple rule}} \cr
& F'\left( t \right) = \frac{d}{{dt}}\left[ {{t^3} + {e^3}} \right] \cr
& {\text{Use the sum diffence rules for differentiation }}\left( {{\text{See page 178}}} \right) \cr
& F'\left( t \right) = \frac{d}{{dt}}\left[ {{t^3}} \right] + \frac{d}{{dt}}\left[ {{e^3}} \right] \cr
& {\text{Apply the rules: }}\frac{d}{{dt}}\left[ {{t^n}} \right] = n{t^{n - 1}}{\text{ and }}\frac{d}{{dt}}\left[ c \right] = 0 \cr
& F'\left( t \right) = 3{t^2} + 0 \cr
& F'\left( t \right) = 3{t^2} \cr} $$
