Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.3 Rules of Differentiation - 3.3 Exercises - Page 151: 44


$f'(x)=9x^{2}+10x+6$ $f"(x)=18x+10$ $f^{(3)}(x)=18$

Work Step by Step

$f(x)=3x^{3}+5x^{2}+6x$ $f'(x)=3(3)x^{3-1}+5(2)x^{2-1}+6x^{1-1}$ $f'(x)=9x^{2}+10x^{1}+6x^{0}$ $f'(x)=9x^{2}+10x+6$ $f"(x)=9(2)x^{2-1}+10x^{1-1}+0$ $f"(x)=18x^{1}+10x^{0}$ $f"(x)=18x+10$ $f^{(3)}(x)=18x^{1-1}+0$ $f^{(3)}(x)=18x^{0}$ $f^{(3)}(x)=18$
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