Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 11 - Section 11.1 - Derivatives of Powers, Sums, and Constant Multiples - Exercises - Page 794: 15

Answer

$\displaystyle \frac{dy}{dx}=12x^{2}+2$ (rules listed in work)

Work Step by Step

SUMMARY: The Power Rule$:\ \ \ \displaystyle \frac{d}{dx}[x^{n}]=n\cdot x^{n-1 }\ \ \ $ Sum Rule: $\displaystyle \ \ \ \frac{d}{dx}[f\pm g](x)=\frac{d}{dx}[f(x)]\pm\frac{d}{dx}[g(x)] $ Constant Multiple Rule:$\ \ \ \displaystyle \frac{d}{dx}[cf(x)]=c\cdot\frac{d}{dx}[f(x)] $ Constant times x:$\ \ \ \displaystyle \frac{d}{dx}(cx)=c\ \ \ $ Constant:$\displaystyle \ \ \ \ \ \frac{d}{dx}(c)=0 $ ------------------ $ \displaystyle \frac{dy}{dx}= \displaystyle \frac{d}{dx}[4x^{3}+2x-1]= ...$Sum Rule$...$ $\displaystyle \frac{dy}{dx}=\frac{d}{dx}[4x^{3}]+\frac{d}{dx}[2x]-\frac{d}{dx}[5]=$... individually: $\displaystyle \frac{d}{dx}[4x^{3}]$=...Constant Multiple Rule...= $=4\displaystyle \cdot\frac{d}{dx}[x^{3}]$=... Power Rule... $=4(3x^{2})=12x^{2}$ $\displaystyle \frac{d}{dx}[2x]$=...Constant times x...=$2$ $\displaystyle \frac{d}{dx}[5]=$...Constant...$=0$ . So, $\displaystyle \frac{dy}{dx}=12x^{2}+2-0$ $\displaystyle \frac{dy}{dx}=12x^{2}+2$
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.