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: 1

Answer

See the attachment.

Work Step by Step

We are given: $f(u)=u^{3/2}$, $g(x)=x^{4}+1$ The composite function is: $f(g(x))=(x^{4}+1)^{3/2}$ Take the derivatives: $f'(u)=\frac{3}{2}u^{\frac{1}{2}}$ $f'(g(x))=\frac{3}{2}(x^{4}+1)^{1/2}$ $g'(x)=4x^{3}$ $(f \circ g)'=f'(g(x))g'(x)$ $=\frac{3}{2}(x^{4}+1)^{1/2}\times 4x^{3}$ $=6x^{3}(x^{4}+1)^{1/2}$ See the filled table below.
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