Answer
$$\frac{{dw}}{{dt}} = 0$$
Work Step by Step
$$\eqalign{
& {\text{Let }}w = xyz,\,\,\,\,x = 2{t^4},\,\,y = 3{t^{ - 1}}\,\,{\text{and }}z = 4{t^{ - 3}} \cr
& {\text{Write }}w{\text{ in terms of }}t \cr
& w = \left( {2{t^4}} \right)\left( {3{t^{ - 1}}} \right)\left( {4{t^{ - 3}}} \right) \cr
& w = 24{t^{4 - 4}} \cr
& w = 24 \cr
& {\text{Find }}\frac{{dw}}{{dt}} \cr
& \frac{{dw}}{{dt}} = \frac{d}{{dt}}\left[ {24} \right] \cr
& \frac{{dw}}{{dt}} = 0 \cr} $$
