Answer
First Derivative: $r'=\frac{-2}{3s^{3}}+\frac{5}{2s^{2}}$
Second Derivative: $r''=\frac{2}{s^{4}}-\frac{5}{s^{3}}$
Work Step by Step
Using the Power Rule:
First Derivative:
$r=\frac{1}{3s^{2}}-\frac{5}{2s}$
$r'=(-2)(\frac{1}{3})s^{-2-1}-(-1)(\frac{5}{2})s^{-1-1}$
$r'=\frac{-2}{3}s^{-3}+\frac{5}{2}s^{-2}$
$r'=\frac{-2}{3s^{3}}+\frac{5}{2s^{2}}$
Second Derivative:
$r'=\frac{-2}{3}s^{-3}+\frac{5}{2}s^{-2}$
$r''=(-3)\frac{-2}{3}s^{-3-1}+(-2)\frac{5}{2}s^{-2-1}$
$r''=2s^{-4}-5s^{-3}$
$r''=\frac{2}{s^{4}}-\frac{5}{s^{3}}$
