Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.3 - Derivatives of Trigonometric Functions - 3.3 Exercises: 2

Answer

$f'(x)=-x\sin x+\cos x+2\sec^{2}x$

Work Step by Step

$f(x)=x\cos x+2\tan x$ Differentiate each term: $f'(x)=(x\cos x)'+(2\tan x)'=...$ Use the product rule to differentiate $x\cos x$ $...=(x)(\cos x)'+(\cos x)(x)'+2\sec^{2}x=...$ $...=-x\sin x+\cos x+2\sec^{2}x$
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