Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.3 Differentiation Formulas - 2.3 Exercises - Page 141: 60


$G'(r)=\dfrac{1}{2}r^{-1/2}+\dfrac{1}{3}r^{-2/3}$ $G''(r)=-\dfrac{1}{4}x^{-3/2}-\dfrac{2}{9}r^{-5/3}$

Work Step by Step

Rewrite the function $G(r)=\sqrt{r}+\sqrt[3] r=r^{1/2}+r^{1/3}$ Apply power rule to the function to find the first derivate $G'(r)=(\dfrac{1}{2})r^{1/2-1}+(\dfrac{1}{3})r^{1/3-1}$ $G'(r)=\dfrac{1}{2}r^{-1/2}+\dfrac{1}{3}r^{-2/3}$ Apply power rule the first derivate to find the second derivate $G''(r)=\dfrac{1}{2}(-\dfrac{1}{2})r^{-1/2-1}+\dfrac{1}{3}(-\dfrac{2}{3})r^{-2/3-1}$ $G''(r)=-\dfrac{1}{4}x^{-3/2}-\dfrac{2}{9}r^{-5/3}$
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