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: 15

Answer

$y=f[g(x)],$ $f(x)=x^{3/5},\qquad g(x)=5-x^{2}$

Work Step by Step

A reliable method is asking: "How would we calculate this on a calculator?". First, calculate $g(x)=5-x^{2}$ and then, calculate: $\quad [$the result, g(x) $]^{3/5}$ (apply $f(x)=x^{3/5}$ on g(x) instead of x) $f[g(x)]=(g(x))^{3/5}=(5-x^{2})^{3/5}=y$
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