Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 6 - Inverse Functions - Review - Exercises - Page 505: 53

Answer

$$f^{(n)}(x) = 2^x(\ln 2)^n$$

Work Step by Step

Given $f(x)= 2^x$ Then \begin{align*} f'(x)&= 2^x\ln 2\\ f''(x)&= 2^x(\ln 2)^2\\ f'''(x)&= 2^x(\ln 2)^3\\ \vdots\ \ \ &=\vdots\\ f^{(n)}(x)&= 2^x(\ln 2)^n\\ \end{align*}
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