University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Questions to Guide Your Review - Page 201: 8


Power rule of a polynomial function: $p(x)=a_{n}x^n+a_{n-1}x^{(n-1)}+......+a_{0}$ $p'(x)=na_{n}x^{(n-1)}+(n-1)(a_{n-1}x^{(n-2)})+...+(a_{1})$

Work Step by Step

Given the following polynomial function: $p(x)=a_{n}x^n+a_{n-1}x^{(n-1)}+......+a_{0}$ We find the derivative using the power rule thus: $p'(x)=na_{n}x^{(n-1)}+(n-1)(a_{n-1}x^{(n-2)})+...+(a_{1})$ In addition, we know the sum rule, product rule, quotient rule, etc.
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