Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 5 - Graphs and the Derivative - 5.3 Higher Derivatives, Concavity, and the Second Derivative Test - 5.3 Exercises - Page 283: 26

Answer

$$ f(x)=e^{x}, $$ To find the second derivative of find the first derivative, and then take its derivative. $$ f^{\prime}(x)=e^{x}, $$ $$ f^{\prime\prime}(x)=e^{x}, $$ $$ f^{\prime\prime\prime}(x)=e^{x}, $$ and so on $$ f^{(n)}(x)=e^{x}, $$

Work Step by Step

$$ f(x)=e^{x}, $$ To find the second derivative of find the first derivative, and then take its derivative. $$ f^{\prime}(x)=e^{x}, $$ $$ f^{\prime\prime}(x)=e^{x}, $$ $$ f^{\prime\prime\prime}(x)=e^{x}, $$ and so on $$ f^{(n)}(x)=e^{x}, $$
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