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: 27

Answer

\[\frac{{dy}}{{dx}} = - 2\cos x\sin x\]

Work Step by Step

\[\begin{gathered} y = {\cos ^2}x \hfill \\ \hfill \\ or \hfill \\ y = \left( {\cos x} \right)\left( {\cos x} \right) \hfill \\ \hfill \\ \,\,use\,\,the\,\,product\,\,rule. \hfill \\ \hfill \\ \frac{{dx}}{{dy}} = 2\left( {\cos x\,} \right)\,{\left( {\cos x} \right)^\prime } + \left( {\cos x\,} \right)\,{\left( {\cos x} \right)^\prime } \hfill \\ \hfill \\ \frac{{dx}}{{dy}} = 2\,\left( {\cos x\,} \right)\,{\left( {\cos x} \right)^\prime } \hfill \\ \hfill \\ then \hfill \\ \hfill \\ \frac{{dx}}{{dy}} = 2\,\cos x\,\left( { - \sin x} \right) \hfill \\ \hfill \\ simplify \hfill \\ \hfill \\ \frac{{dy}}{{dx}} = - 2\cos x\sin x \hfill \\ \hfill \\ \end{gathered} \]
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