Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 3 - Derivatives - 3.5 Derivatives of Trigonometric Functions - 3.5 Exercises: 48

Answer

$y''=-4\sin\theta\cos\theta$

Work Step by Step

$y=\cos\theta\sin\theta$ Apply the product rule to find the first derivative: $y'=\cos\theta(\sin\theta)'+\sin\theta(\cos\theta)'=...$ Evaluate the derivatives indicated and simplify: $...=(\cos\theta)(\cos\theta)+(\sin\theta)(-\sin\theta)=\cos^{2}\theta-\sin^{2}\theta$ The expression above is the first derivative. Evaluate the second derivative by differentiating the first derivative found: $y''=2\cos\theta(\cos\theta)'-2\sin\theta(\sin\theta)'=...$ Evaluate the derivatives indicated and simplify: $...=2(\cos\theta)(-\sin\theta)-2(\sin\theta)(\cos\theta)=...$ $...=-2\sin\theta\cos\theta-2\sin\theta\cos\theta=-4\sin\theta\cos\theta$ The expression above is the second derivative.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.