Thomas' Calculus 13th Edition

First Derivative: s' = 15$t^{2}$ - 15$t^{4}$ Second Derivative: s'' = 30$t$ - 60$t^{3}$
Using the power rule: Work with the first and second term separately First Derivative: s = 5$t^{3}$ - 3$t^{5}$ s' = (3)(5)$t^{2}$ - (5)(3)$t^{4}$ s' = 15$t^{2}$ - 15$t^{4}$ Second Derivative: s' = 15$t^{2}$ - 15$t^{4}$ s'' = (2)(15)$t$ - (4)(15)$t^{3}$ s'' = 30$t$ - 60$t^{3}$