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: 40

Answer

\[\frac{{dy}}{{d\theta }} = - 2{\csc ^3}\theta \,\cot \,\theta \]

Work Step by Step

\[\begin{gathered} y = {\csc ^2}\theta - 1 \hfill \\ \hfill \\ differentiate\,using\,\,the\,chain\,\,rule: \hfill \\ \hfill \\ \frac{{dy}}{{d\theta }} = 2{\csc ^2}\theta \,{\left( {\csc \,\,\theta } \right)^\prime } \hfill \\ \hfill \\ \frac{{dy}}{{d\theta }} = 2{\csc ^2}\theta \,\left( { - \csc \,\theta \,\cot \theta } \right) \hfill \\ \hfill \\ multiply \hfill \\ \hfill \\ \frac{{dy}}{{d\theta }} = - 2{\csc ^3}\theta \,\cot \,\theta \hfill \\ \end{gathered} \]
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