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: 6

Answer

(a)$F'(-1)=-12$ (b)$G'(-1)=-15$

Work Step by Step

(a)$F(x)=f(g(x))$ $F'(x)=f'(g(x))\times{g'(x)}$ $F'(-1)=f'(g(-1))\times{g'(-1)}$ $F'(-1)=f'(2)\times{-3}$ $F'(-1)=4\times{-3}$ $F'(-1)=-12$ (b)$G(x)=g(f(x))$ $G'(x)=g'(f(x))\times{f'(x)}$ $G'(-1)=g'(f(-1))\times{f'(-1)}$ $G'(-1)=g'(2)\times{3}$ $G'(-1)=-5\times{3}$ $G'(-1)=-15$
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