Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 2 - Differentiation - 2.2 Exercises: 24

Answer

The derivative is $\frac{-5}{4x^4}-2sin(x)$.

Work Step by Step

This question requires you to use every trick you've used till now. The overall derivative is the sum of the derivatives of the mini functions. $\frac{5}{8x^3}$ can be rewritten as $\frac{5x^{-3}}{8}$ whose derivative is $\frac{-4*5x^{-4}}{8}$ which simplifies to $\frac{-5}{4x^4}$. The second part of the question is since the derivative of $cos(x)$ is $-sin(x)$, hence the derivative of $2cos(x)$ is $-2sin(x)$. The overall derivative then is $\frac{-5}{4x^4}-2sin(x)$.
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.