Calculus 8th Edition

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

Chapter 6 - Inverse Functions - 6.2* The Natural Logarithmic Functions - 6.2* Exercises: 17

Answer

$x^2(1+3\ln x)$

Work Step by Step

$\frac{d}{dx}x^3\ln x$ $=x^3\frac{d}{dx}\ln x+\ln x\frac{d}{dx}x^3$ $=x^3*\frac{1}{x}+\ln x*3x^2$ $=x^2+3x^2\ln x$ $=x^2(1+3\ln x)$
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