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: 20


$y=f[g(x)],$ $f(x)=x^{2}+x+5,\qquad g(x)=x^{1/2}-3$

Work Step by Step

A reliable method is asking: "How would we calculate this on a calculator?". First, calculate $g(x)=x^{1/2}-3$ and then, calculate: $\quad [g(x)]^{2}+ [g(x)]+5$ (apply $f(x)=x^{2}+x+5\quad $ on g(x) instead of x) $f[g(x)]=[g(x)]^{2}+ [g(x)]+5$ $=(x^{1/2}-3)^{2}+(x^{1/2}-3)+5$ $=y$
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