Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.3 Differentiation Formulas - 2.3 Exercises - Page 140: 23


Yes, the answers agree.

Work Step by Step

Product Rule: $f(x)=(1+2x^2)(x-x^2)$ $f'(x)=(1+2x^2)(1-2x)+(x-x^2)(0+4x)$ $f'(x)=(1-2x+2x^2-4x^3)+(4x^2-4x^3)$ $f'(x)=-8x^3+6x^2-2x+1$ Performing Multiplication First: $f(x)=(1+2x^2)(x-x^2)$ $f(x)=x-x^2+2x^3-2x^4$ $f'(x)=1-2x+6x^2-8x^3=-8x^3+6x^2-2x+1$ Therefore, the answers agree.
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