Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 3: Derivatives - Section 3.5 - Derivatives of Trigonometric Functions - Exercises 3.5: 2

Answer

The Derivative is: $y'=-\frac{3}{x^2}+5\cos x$

Work Step by Step

$y=\frac{3}{x}+5\sin x$ $y=3x^{-1}+5\sin x$ Applying Derivative Rules: $y'=f'(x)+g'(x)$ $y'=(-1)(3)x^{-1-1}+(5)(\cos x)$ $y'=-3x^{-2}+5\cos x$ $y'=-\frac{3}{x^2}+5\cos x$
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