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


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