Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.6 The Chain Rule - Exercises Set 2.6: 8

Answer

$f'(x)=6 (3x^2+2x-1)^5 (6x+2) $

Work Step by Step

Given that $f(x)=(3x^2+2x−1)^6$ We can write this as $ f (x)=(g (x))^6$, where $ f (x)$ is the outside function and $ g ( x ) = 3x^2+2x-1$ is the inside function. To find the answer we need to differentiate the outside function $ f(x) $ and times it by the derivative of the inside function $ g (x)$. $f(x)=(3x^2+2x−1)^6$ $ f (x)=(g (x))^6$ $f'(x)=6(g ( x ))^{6-1}×(g' ( x )) $ $f'(x)=6(g ( x ))^{5}×(6x^{2-1}+2) $ $f'(x)=6(3x^2+2x−1)^{5}×(6x^{1}+2) $ $f'(x)=6(3x^2+2x−1)^{5}(6x+2) $
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