Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.2 - The Product and Quotient Rules - 3.2 Exercises: 12

Answer

$f'(z)=-ze^{z}-2e^{2z}+1$

Work Step by Step

$f(z)=(1-e^{z})(z+e^{z})$ Differentiate using the product rule $f'(z)=(1-e^{z})(z+e^{z})'+(z+e^{z})(1-e^{z})'=...$ $...=(1-e^{z})(1+e^{z})+(z+e^{z})(-e^{z})=...$ Evaluate the products and simplify $...=1-e^{2z}-ze^{z}-e^{2z}=-ze^{z}-2e^{2z}+1$
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