Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.7 The Chain Rule - Exercises - Page 145: 2

Answer

See the attachment.

Work Step by Step

Given: $f(u)=u^{3}$, $g(x)=3x+5$ We find the composite function as follows: $f(g(x))=(3x+5)^{3}$ Now, take the derivatives: $f'(u)= 3u^{3-1}=3u^{2}$ $f'(g(x))=3(3x+5)^{2}$ $g'(x)=3$ $(f\circ g)'=f'(g(x))\times g'(x)$ $=3(3x+5)^{2}\times3=9(3x+5)^{2}$ See the filled table below.
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