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: 14

Answer

$y' = 3x^2\ln x + x^2$

Work Step by Step

In order to derivate this function you have to apply the product rule $\dfrac{d}{dx}(ab)= a'b+ab'$ Identify the functions a and b, and derivate them $a=x^3$ $a'=3x^2$ $b=\ln x$ $b'=\dfrac{1}{x}$ Then undo the substitution, simplify and get the answer: $y' = (3x^2)(\ln x)+(x^3)(\dfrac{1}{x})$ $y' = 3x^2\ln x + x^2$
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