Calculus 10th Edition

by Larson, Ron; Edwards, Bruce H.

Published by Brooks Cole

ISBN 10: 1-28505-709-0

ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.3 Exercises - Page 125: 1

Answer

The derivative is $4x^3-12x^2+6x-12$.

Work Step by Step

Product Rule: $g'(x)=((u(x)(v(x))’=u'(x)v(x)+u(x)v’(x))$ $u(x)=(x^2+3) ;u’(x)=(2x) $ $v(x)=(x^2-4x) ;v’(x)=(2x-4) $ $g'(x)=(2x)(x^2-4x)+(x^2+3)(2x-4)=$ $(2x^3-8x^2)+(2x^3+6x-4x^2-12)=$ $4x^3-12x^2+6x-12$

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