Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.5 Derivatives of Trigonometric Functions - Exercises Set 2.5: 2

Answer

$=-\frac{10}{x^{3}}+cosx$

Work Step by Step

Convert the polynomial into a power of $x$, giving you $5x^{-2}$, Finally, split the derivative into two separate, single derivatives. The polynomial derivative uses power rule ($[x^{n}]'=nx^{n-1}$) while the derivative of $sinx$ is $cosx$. Therefore, the derivative is $-5(2){x^{-2-1}}+cosx=-\frac{10}{x^{3}}+cosx.$
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