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 - Page 817: 10

Answer

In both cases (a. and b.): $t^{\prime}(x)=\displaystyle \frac{1}{3}$

Work Step by Step

a. $ t(x)=\displaystyle \frac{x}{3}=\frac{1}{3}\cdot x\qquad$ (constant multiple) $t^{\prime}(x)=\displaystyle \frac{1}{3}(1)=\frac{1}{3}$ b. $u(x)=x ,\displaystyle \ \ \ v(x)=3,\ \ \ s(x)=\frac{u(x)}{v(x)}$ $u^{\prime}(x)=1,\ \ \ v^{\prime}(x)=0$ Quotient Rule: $t^{\prime}(x)=\displaystyle \frac{u^{\prime}(x)v(x)-u(x)v^{\prime}(x)}{[v(x)]^{2}}=$ $= \displaystyle \frac{1\cdot 3-0(x)}{3^{2}}=\frac{3}{9}=\frac{1}{3}$
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