Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.6 The Chain Rule - Exercises Set 2.6: 3

Answer

$(a) (f\circ g)(x)=(2x-3)^5, (f\circ g)'(x)=10(2x-3)^4$ $(b) (g \circ f)(x)=2x^5-3, (g\circ f)'(x)=10x^4$

Work Step by Step

$f(x)=x^5, g(x)=2x-3$ $(a)$ $(f \circ g)(x)=f(g(x))=f(2x-3)=(2x-3)^5$ $(f\circ g)'(x)=((2x-3)^5)'=5(2x-3)^4\cdot(2x-3)'=5(2x-3)^4\cdot2=10(2x-3)^4$ $(b) (g\circ f)(x)=g(f(x))=g(x^5)=2x^5-3$ $(g\circ f)'(x)=(2x^5-3)'=2\cdot5x^4-0=10x^4$
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