Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.1 Exercises - Page 325: 46


$2x\ln x+x$

Work Step by Step

By theorem 5.3/$1$:$\ \ \ \displaystyle \frac{d}{dx}[\ln x]=\frac{1}{x}$ $y=x^{2}\cdot\ln x$ We use the product rule here: $y^{\prime}=(x^{2})^{\prime}\cdot\ln x+x^{2}\cdot(\ln x)^{\prime}$ $=2x\displaystyle \ln x+x^{2}\cdot\frac{1}{x}$ $=2x\ln x+x$
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