Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.5 Higher Derivatives - Exercises - Page 135: 12


$$ y''=20x^3+12x^2+2, \quad y'''=60x^2+24x.$$

Work Step by Step

Let $ y=(x^2+x)(x^3+1)$; first we simplify $ y $ as follows $$ y=(x^2+x)(x^3+1)=x^5+x^4+x^2+x.$$ Now, we get $$ y'=5x^4+4x^3+2x+1$$ $$ y''=20x^3+12x^2+2, \quad y'''=60x^2+24x.$$
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