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 818: 40


$1.1(x^{2.1}-x)(3.4-x^{-2.1})+ (1.1x+4)(2.1x^{1.1}-1)(3.4-x^{-2.1})+(1.1x+4)(x^{2.1}-x)\cdot 2.1x^{-3.1}$

Work Step by Step

Using the more general product rule (example 1b), $(f\cdot g\cdot h)^{\prime}=f^{\prime}gh+fg^{\prime}h+fgh^{\prime}$ $f(x)=1.1x+4,\qquad f^{\prime}(x)=1.1$ $g(x)=x^{2.1}-x,\qquad g^{\prime}(x)=2.1x^{1.1}-1$ $h(x)=3.4-x^{-2.1},\qquad $ $h^{\prime}(x)=-(-2.1x^{-3.1})=2.1x^{-3.1}$ $\displaystyle \frac{dy}{dx}=(f\cdot g\cdot h)^{\prime}(x)=$ $=1.1(x^{2.1}-x)(3.4-x^{-2.1})+ (1.1x+4)(2.1x^{1.1}-1)(3.4-x^{-2.1})+(1.1x+4)(x^{2.1}-x)\cdot 2.1x^{-3.1}$ ... we do not need to expand the answer
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