Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.4 Exercises: 16

Answer

$f'(x)=\dfrac{4}{\sqrt[3]{(12x-5)^2}}.$

Work Step by Step

$u=(12x-5)$; $\dfrac{du}{dx}=12$ $f(u)=u^{\frac{1}{3}};\dfrac{d}{du}f(u)=\dfrac{1}{3\sqrt[3]{u^2}}.$ $\dfrac{d}{dx}f(x)=\dfrac{d}{du}f(u)\times\dfrac{du}{dx}=(12)\dfrac{1}{3\sqrt[3]{(12x-5)^2}}=\dfrac{4}{\sqrt[3]{(12x-5)^2}}.$
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