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: 3


See the attachment.

Work Step by Step

We are given: $f(u)=\tan u$, $g(x)=x^{4}$ The composite function is: $f(g(x))=\tan(x^{4})$ Take the derivatives: $f'(u)=\sec^{2}u$ $f'(g(x))=\sec^{2} (x^{4})$ $g'(x)=4x^{3}$ $(f \circ g)'=f'(g(x))g'(x)$ $=\sec^{2}(x^{4})\times 4x^{3}$ $=4x^{3}\sec^{2}(x^{4})$ See the filled table below.
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