Chapter 3 - Section 3.3 - Differentiation Rules - Exercises - Page 136: 46

$s' = \frac{-5t+2}{t^{3}}$ $s'' = \frac{2(5t-3)}{t^{4}}$

$s = \frac{t^{2}+5t-1}{t^{2}}$ $s' = \frac{t^{2}(2t+5) - 2t(t^{2}+5t-1)}{t^{4}}$ $s' = \frac{-5t^{2}+2t}{t^{4}}$ $s' = \frac{-5t+2}{t^{3}}$ $s'' = \frac{t^{3}(-5)-3t^{2}(-5t+2)}{t^{6}}$ $s'' = \frac{10t^{3}-6t^{2}}{t^{6}}$ $s'' = \frac{10t-6}{t^{4}}$ $s'' = \frac{2(5t-3)}{t^{4}}$