Calculus 10th Edition

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

Chapter 2 - Differentiation - 2.4 Exercises: 86

Answer

$f''(x)=432x^7+2160x^4+1728x.$

Work Step by Step

Using the Chain Rule: $f'(x)=(6)(3x^2)(3)(x^3+4)^{3-1}=54x^2(x^3+4)^2$. Using the Product Rule and the Chain Rule: Product Rule $(f'’(x)=(u(x)(v(x))’=u’(x)v(x)+u(x)v’(x))$ $u(x)=54x^2 ;u’(x)= 108x$ $v(x)= (x^3+4)^2;v’(x)=6x^2(x^3+4) $ $f''(x)=(108x)(x^3+4)^2+(54x^2)(6x^2(x^3+4))$ $=432x^7+2160x^4+1728x$.
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