University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Section 3.3 - Differentiation Rules - Exercises: 22

Answer

$\frac{dw}{dx}=-\frac{17}{(2x-7)^2}$

Work Step by Step

We are given that $w=(2x-7)^{-1}(x+5)$ $\implies w=\frac{x+5}{2x-7}$ Differentiating both sides and applying the quotient rule, we obtain: $\frac{dw}{dx}=\frac{(2x-7)(x+5)^{\prime}-(x+5)(2x-7)^{\prime}}{(2x-7)^2}$ $\implies \frac{dw}{dx}=\frac{(2x-7)(1)-(x+5)(2)}{(2x-7)^2} $ $\implies \frac{dw}{dx}=\frac{2x-7-2x-10}{(2x-7)^2}$ $\implies \frac{dw}{dx}=-\frac{17}{(2x-7)^2}$
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