Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 2 - The Derivative - 2.5 Derivatives of Trigonometric Functions - Exercises Set 2.5 - Page 151: 7

Answer

$$f'\left( x \right) = \sec x\tan x - \sqrt 2 {\sec ^2}x$$

Work Step by Step

$$\eqalign{ & f\left( x \right) = \sec x - \sqrt 2 \tan x \cr & {\text{find the derivative}} \cr & f'\left( x \right) = \left( {\sec x - \sqrt 2 \tan x} \right)' \cr & {\text{sum rule}} \cr & f'\left( x \right) = \left( {\sec x} \right)' - \left( {\sqrt 2 \tan x} \right)' \cr & f'\left( x \right) = \left( {\sec x} \right)' - \sqrt 2 \left( {\tan x} \right)' \cr & {\text{use basic formulas }} \cr & f'\left( x \right) = \sec x\tan x - \sqrt 2 \left( {{{\sec }^2}x} \right) \cr & f'\left( x \right) = \sec x\tan x - \sqrt 2 {\sec ^2}x \cr} $$
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