Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.4 Derivatives of Trigonometric Functions - 2.4 Exercises - Page 150: 8


Differentiate $y = u(a\cos u + b\cot u)$ $y'=a\cos u + b\cot u -au\sin u -bu\csc ^2u$

Work Step by Step

The equation given is $y = u(a\cos u + b\cot u)$. Use the product rule and the trig rules. $y' = u'(a\cos u + b\cot u) + u(a\cos u + b\cot u)'$ $=(a\cos u + b\cot u) + u(-a\sin u -b\csc ^2u)$ $=a\cos u + b\cot u -au\sin u -bu\csc ^2u$
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