Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.5 The Chain Rule - 2.5 Exercises: 9

Answer

f'(x) = $\frac{5}{2}(5x + 1)^{-1/2}$

Work Step by Step

To find the derivative of f(x), we can first realize that $\sqrt(5x + 1)$ is the same thing as $(5x + 1)^{1/2}$ From there we need to identify the inside and outside functions. The inside function is 5x + 1 The outside function is $u^{1/2}$ We know from the chain rule that f'(x) will be equal to the derivative of the outside function multiplied by the inside function: f'(x) = $\frac{1}{2}(5x + 1)^{-1/2}(5)$ which is the same thing as f'(x) = $\frac{5}{2}(5x + 1)^{-1/2}$
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