Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.3 Exercises: 36

Answer

$f'(x)=7x^6+6x^5+4x^3-9x^2-4x+2$

Work Step by Step

Product Rule: $f′(x)=((u(x)(v(x)w(x))′=u′(x)v(x)w(x)+u(x)v′(x)w(x)$ $+u(x)v(x)w′(x)$ $u(x)=(x^3-x);u′(x)=(3x^2-1)$ $v(x)=(x^2+2);v′(x)=2x$ $w(x)=(x^2+x-1);w′(x)=(2x+1)$ $f'(x)=(3x^2-1)(x^2+2)(x^2+x-1)+$ $(x^3-x)(2x)(x^2+x-1)+(x^3-x)(x^2+2)(2x+1)=$ $3x^6+5x^4−2x^2+3x^5+5x^3−2x−3x^4−5x^2+2+2x^6$ $−2x^4+2x^5−2x^3−2x^4+2x^2+2x^6+2x^4−4x^2+x^5+x^3$ $−2x=7x^6+6x^5+4x^3-9x^2-4x+2$
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