Answer
$$\frac{{dy}}{{dx}} = - 60{x^2}{e^{4{x^3}}}$$
Work Step by Step
$$\eqalign{
& y = - 5{e^{4{x^3}}} \cr
& {\text{find the derivative of the function}} \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ { - 5{e^{4{x^3}}}} \right] \cr
& {\text{use multiple constant rule }}\frac{d}{{dx}}\left[ {kg\left( x \right)} \right] = k\frac{d}{{dx}}\left[ {g\left( x \right)} \right] \cr
& \frac{{dy}}{{dx}} = - 5\frac{d}{{dx}}\left[ {{e^{4{x^3}}}} \right] \cr
& {\text{use the formula }}\frac{d}{{dx}}\left( {{e^{g\left( x \right)}}} \right) = {e^{g\left( x \right)}}g'\left( x \right).{\text{ we can see that }}g\left( x \right) = 4{x^3}.{\text{ then}} \cr
& \frac{{dy}}{{dx}} = - 5{e^{4{x^3}}}\frac{d}{{dx}}\left[ {4{x^3}} \right] \cr
& \frac{{dy}}{{dx}} = - 5{e^{4{x^3}}}\left( {12{x^2}} \right) \cr
& {\text{multiply}} \cr
& \frac{{dy}}{{dx}} = - 60{x^2}{e^{4{x^3}}} \cr} $$
