Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.4 - The Chain Rule - 3.4 Exercises: 9

Answer

$f'(x)=\dfrac{5}{2\sqrt{5x+1}}$

Work Step by Step

$f(x)=\sqrt{5x+1}$ Let's write the function like this: $f(x)=(5x+1)^{1/2}$ Differentiate using the chain rule: $f'(x)=\dfrac{1}{2}(5x+1)^{-1/2}(5x+1)'=...$ $...=\dfrac{1}{2}(5x+1)^{-1/2}(5)=\dfrac{5}{2}(5x+1)^{-1/2}=\dfrac{5}{2(5x+1)^{1/2}}=...$ $...=\dfrac{5}{2\sqrt{5x+1}}$
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