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: 35

Answer

$f'(x)=10x^4-8x^3-21x^2-10x-30.$

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)=(2x^3+5x) ;u’(x)=(6x^2+5) $ . $v(x)=(x-3) ;v’(x)=1 $ . $w(x)=(x+2);w'(x)=1$ . $f'(x)=(x+2)(2x^3+5x)+(x-3)(2x^3+5x)$ $+(x-3)(x+2)(6x^2+5)=10x^4-8x^3-21x^2-10x-30.$
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