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: 5

Answer

(a) $F'(3)=-7$ (b)$G'(3)=-8$

Work Step by Step

(a)$F(x)=f(g(x))$ $F'(x)=f'(g(x))\times{g'(x)}$ $F'(3)=f'(g(3))\times{g'(3)}$ $F'(3)=f'(5)\times{7}$ $F'(3)=-1\times{7}$ $F'(3)=-7$ (b)$G(x)=g(f(x))$ $G'(x)=g'(f(x))\times{f'(x)}$ $G'(3)=g'(f(3))\times{f'(3)}$ $G'(3)=g'(5)\times{-2}$ $G'(3)=4\times{-2}$ $G'(3)=-8$
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