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: 6

Answer

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)
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.