Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.2 Derivatives And Integrals Involving Logarithmic Functions - Exercises Set 6.2: 13

Answer

$dy/dx=\ln(x)+1$

Work Step by Step

Using the product rule for derivatives ($[uv]'=u'v+uv'$), the derivative of $xln(x)$ equals $(x)'ln(x)+x(ln(x))'$=$ln(x)+\frac{x}{x}=\boxed{\ln(x)+1}$.
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