Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Section 3.3 Differentiation Rules - Exercises 3.3 - Page 125: 6


First Derivative: $y'=x^{2}+x+\frac{1}{4}$ Second Derivative: $y''=2x+1$

Work Step by Step

Using the power rule: First Derivative: $y=\frac{x^{3}}{3}+\frac{x^{2}}{2}+\frac{x}{4}$ $y'=\frac{(3)x^{3-1}}{3}+\frac{(2)x^{2-1}}{2}+\frac{(1)x^{1-1}}{4}$ $y'=x^{2}+x+\frac{1}{4}$ Second Derivative: $y'=x^{2}+x+\frac{1}{4}$ $y''=(2)x^{2-1}+(1)x^{1-1}+(0)$ $y''=2x+1$ (the derivative of $\frac{1}{4}$ will be 0 because of the rule of the constant function)
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