Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 4 - Calculating the Derivative - 4.1 Techniques for Finding Derivatives - 4.1 Exercises - Page 207: 27

Answer

$$ D_{x}\left[9 x^{-1 / 2}+\frac{2}{x^{-3 / 2}}\right]=\frac{-9}{2} x^{-3 / 2}-3 x^{-5 / 2} $$

Work Step by Step

\begin{align*} D_{x}\left[9 x^{-1 / 2}+\frac{2}{x^{-3 / 2}}\right]&=D_{x}\left[9 x^{-1 / 2}\right]+D_{x}\left[\frac{2}{x^{-3 / 2}}\right]\\ &=\frac{d}{dx}\left[9 x^{-1 / 2}\right]+\frac{d}{dx}\left[ 2 x^{ 3 / 2 }\right] ,\ \ \left(\text{Use } \frac{d}{dx} (x^n)=2x^{n-1}\right) \\ &=\frac{-9}{2} x^{-3 / 2}-3 x^{-5 / 2}\\ \end{align*}
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.