Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises: 29

Answer

f'(x)=$\ln$(x)+1

Work Step by Step

To differentiate the function y=x$\ln$(x) we will use the product rule which states that if f(x)=h(x)g(x), then f'(x)=g(x)h'(x)+h(x)g'(x). Therefore, we'll set h(x)=x and g(x)=$\ln$(x) and apply the product rule. Therefore, f'(x)=$\ln$(x)$\frac{d}{dx}$[x]+(x)$\frac{d}{dx}$[$\ln$(x)] $\frac{d}{dx}$[x]=1, using the power rule $\frac{d}{dx}$[$\ln$(x)]=$\frac{1}{x}$, according to the rule of the derivative of a natural log function f'(x)=$\ln$(x)+1
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