Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.4 Derivatives of Logarithmic Functions - 6.4 Exercises: 58

Answer

$\frac{8!}{x}$

Work Step by Step

Find $\frac{d^{9}}{dx^{9}}(x^{8}lnx)$. Consider $y=(x^{8}lnx)$ $y'=x^{8}\times\frac{1}{8}+8x^{7}lnx$ $y''=15x^{6}+8.7x^{6}lnx$ $y'''=14x^{5}+8.7.6x^{5}lnx$ Proceeding in the same manner, we will have 9th times derivative of the given function. $y^{9}=\frac{8!}{x}$ Hence, $\frac{d^{9}}{dx^{9}}(x^{8}lnx)=\frac{8!}{x}$
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