Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 4 - Calculating the Derivative - 4.3 The Chain Rule - 4.3 Exercises - Page 225: 16


$y=f[g(x)],$ $f(x)=x^{2/3},\qquad g(x)=3x^{2}-7$

Work Step by Step

A reliable method is asking: "How would we calculate this on a calculator?". First, calculate $g(x)=3x^{2}-7$ and then, calculate: $\quad [$the result, g(x) $]^{2/3}$ (apply $f(x)=x^{2/3}$ on g(x) instead of x) $f[g(x)]=[g(x)]^{2/3}=(3x^{2}-7)^{2/3}=y$
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