Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 3 - Differentiation - 3.6 Trigonometric Functions - Exercises - Page 140: 40


\begin{align*} \frac{d^2 }{dt^2} \cos^2 t&=-2\cos 2t . \end{align*}

Work Step by Step

We have \begin{align*} \frac{d}{dt} \cos^2 t&=2\cos t (-\sin t)\\ &=-2\sin t \cos t\\ &=-\sin 2t \end{align*} and hence \begin{align*} \frac{d^2 }{dt^2} \cos^2 t&=-\frac{d}{dt} \sin 2 t\\ &=-2\cos 2t . \end{align*}
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