Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.3 Differentiation Formulas - 2.3 Exercises - Page 141: 45


P'(x) = n$a_{n}x^{n-1}$ + (n-1)$a_{n-1}x^{n-2}$ + $\cdot$ $\cdot$ $\cdot$ + 3$a_{3}x^{2}$ + 2$a_{2}x$ + $a_{1}$

Work Step by Step

We take the derivative term by term. Each term is of the form $ax^{n}$, by the power rule the derivative should be $anx^{n-1}$. The only term that is different is $a_{0}$ which is a constant, and the derivative of a constant is 0. So each term is multiplied by its power, then one is subtracted from the power and the constant drops off and we get: P'(x) = n$a_{n}x^{n-1}$ + (n-1)$a_{n-1}x^{n-2}$ + $\cdot$ $\cdot$ $\cdot$ + 3$a_{3}x^{2}$ + 2$a_{2}x$ + $a_{1}$
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