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: 30

Answer

\[ = \sec x\tan x\]

Work Step by Step

\[\begin{gathered} \frac{d}{{dx}}\,\left( {\sec x} \right) = \sec x\tan x \hfill \\ \hfill \\ use\,\,trigonometric\,\,identity{\text{ }}\sec x = \frac{1}{{\cos x}} \hfill \\ \hfill \\ \frac{d}{{dx}}\,\left( {\frac{1}{{\cos x}}} \right) \hfill \\ \hfill \\ then \hfill \\ \hfill \\ \frac{d}{{dx}}\,\left( {\frac{1}{{\cos x}}} \right) = \frac{{ - \left( { - \sin x} \right)}}{{{{\cos }^2}x}} \hfill \\ \hfill \\ or \hfill \\ \hfill \\ = \,\left( {\frac{{\sin x}}{{\cos x}}} \right)\,\left( {\frac{1}{{\cos x}}} \right) \hfill \\ \hfill \\ then \hfill \\ \hfill \\ = \sec x\tan x \hfill \\ \hfill \\ \end{gathered} \]
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.