Answer
$$\frac{{dy}}{{dt}} = \left( {1 - e} \right){t^{ - e}}$$
Work Step by Step
$$\eqalign{
& y = {t^{1 - e}} \cr
& {\text{Find the derivative of }}y{\text{ with respect to }}t \cr
& \frac{{dy}}{{dt}} = \frac{d}{{dt}}\left[ {{t^{1 - e}}} \right] \cr
& {\text{Use the power rule for differentiation }}\frac{d}{{dt}}\left[ {{t^n}} \right] = {t^{n - 1}};\cr
& {\text{ Let }}n = 1 - e.{\text{ Then}}{\text{,}} \cr
& \frac{{dy}}{{dt}} = \left( {1 - e} \right){t^{\left( {1 - e} \right) - 1}} \cr
& {\text{Simplify}} \cr
& \frac{{dy}}{{dt}} = \left( {1 - e} \right){t^{1 - e - 1}} \cr
& \frac{{dy}}{{dt}} = \left( {1 - e} \right){t^{ - e}} \cr} $$
