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: 18


$y=f[g(x)],$ $f(x)=\sqrt{x},\qquad g(x)=9-4x$

Work Step by Step

A reliable method is asking: "How would we calculate this on a calculator?". First, calculate $g(x)=9-4x$ and then, calculate: $\quad \sqrt{\text{the result, g(x)}}$ (apply $f(x)=\sqrt{x}$ on g(x) instead of x) $f[g(x)]=\sqrt{g(x)}=\sqrt{9-4x}=y$
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