Answer
$F'\left( t \right) = 8t - 12$
Work Step by Step
$$\eqalign{
& F\left( t \right) = {\left( {2t - 3} \right)^2} \cr
& {\text{Expand the binomial}} \cr
& F\left( t \right) = 4{t^2} - 12t + 9 \cr
& {\text{Differentiate the function}} \cr
& F'\left( t \right) = \frac{d}{{dt}}\left[ {4{t^2} - 12t + 9} \right] \cr
& {\text{Use the sum and difference rule for differentiation }} \cr
& F'\left( t \right) = \frac{d}{{dt}}\left[ {4{t^2}} \right] - \frac{d}{{dt}}\left[ {12t} \right] + \frac{d}{{dt}}\left[ 9 \right] \cr
& {\text{Use the constant multiple rule}} \cr
& F'\left( t \right) = 4\frac{d}{{dt}}\left[ {{t^2}} \right] - 12\frac{d}{{dt}}\left[ t \right] + \frac{d}{{dt}}\left[ 9 \right] \cr
& {\text{Apply the power rule: }}\frac{d}{{dt}}\left[ {{t^n}} \right] = n{t^{n - 1}}{\text{ and }}\frac{d}{{dt}}\left[ c \right] = 0 \cr
& F'\left( t \right) = 4\left( {2t} \right) - 12\left( 1 \right) + 0 \cr
& F'\left( t \right) = 8t - 12 \cr} $$
