Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 11 - Section 11.3 - The Product and Quotient Rules - Exercises: 7

Answer

$r^{\prime}(x)=210x^{1.1}$

Work Step by Step

a. Using the Power and Constant Multiple rules, $c=100,\quad u(x)=x^{2.1}$ $r^{\prime}(x)=c\cdot u^{\prime}(x)$ $=100\cdot(2.1x^{2.1-1})=210x^{1.1}$ b. $u(x)=100 ,\ \ \ v(x)=x^{2.1}$ $h(x)=u(x)v(x)$ $u^{\prime}(x)=0,\ \ \ v^{\prime}(x)=2.1x^{1.1}$ Product Rule: $r^{\prime}(x)=u^{\prime}(x)v(x)+u(x)v^{\prime}(x)$ $= 0(x^{2.1})+100(2.1x^{1.1})=210x^{1.1}$ In both cases (a and b): $r^{\prime}(x)=210x^{1.1}$
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