Explanation Formula used: Derivatives of the Secant Function: d d x ( sec f ( x ) ) = [ sec f ( x ) ] [ tan f ( x ) ] f ′ ( x ) Derivatives of the Tangent and Generalized Tangent Functions 1. d d x ( tan x ) = sec 2 x 2. d d x ( tan f ( x ) ) = [ sec 2 f ( x ) ] f ′ ( x ) Quotient rule : For any differentiable functions f ( x ) and g ( x ) , f ( x ) g ( x ) = g ′ ( x ) f ( x ) − f ′ ( x ) g ( x ) g ( x ) 2 Calculation: By using the Quotient and Product Rule and the above mentioned formula, the rate of change of y = x tan x sec x with respect to x as follows. d y d x = d d x ( x tan x sec x ) = sec x d d x ( x tan x ) − x tan x d d x ( sec x ) ( sec x ) <

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 12.3, Problem 40E

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To find: The rate of change of y=xtanxsecx with respect to x at x=0.

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Chapter 12.3, Problem 39E

Chapter 12.3, Problem 41E

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Chapter 12 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 12.1 - Prob. 1CQ Ch. 12.1 - Prob. 2CQ Ch. 12.1 - Prob. 3CQ Ch. 12.1 - In Exercises 14, express the angle shown in the...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - Prob. 7E

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The rate of change of y = x tan x sec x with respect to x at x = 0 .

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Chapter 12 Solutions