Explanation of Solution Given: The provided logarithmic function is y = In |sec a + tan z| Formula used: (F(9(z))) = f'(g(z)). g'(x) Calculation: Applying the Chain Rule, (|sec a + tan æ|)' y' sec z+ tan z sec z+tan z sec z+tan z| sOc z +tan z )(sec x tan x + sec² x) sec z+tan z| )(sec a + tan æ)' y' sec z+tan z| y' sec z+tan z| sec z+tan z (sec z tan z + sec? x) y' sec z+ tan z| (sec'z+tan z)(sec z tan z+sec?z) y' Isec z+ tan z? E Chapter 3.4, Problem 91E Chapter 3.4, Problem 93E → ||

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.4: Solving Nonlinear Equations
Problem 17E: Van der Waals Equation In Exercise 18 at the end of Section 2.3, we discussed the ideal gas law,...
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Where did they get sec2 in the highlighted area?

Explanation of Solution
Given: The provided logarithmic function is y = In |sec a + tan z|
Formula used:
(F(9(z))) = f'(g(z)). g'(x)
Calculation:
Applying the Chain Rule,
(|sec a + tan æ|)'
y'
sec z+ tan z
sec z+tan z
sec z+tan z|
sOc z +tan z )(sec x tan x + sec² x)
sec z+tan z|
)(sec a + tan æ)'
y'
sec z+tan z|
y'
sec z+tan z|
sec z+tan z (sec z tan z + sec? x)
y'
sec z+ tan z|
(sec'z+tan z)(sec z tan z+sec?z)
y'
Isec z+ tan z?
E Chapter 3.4, Problem 91E
Chapter 3.4, Problem 93E →
||
Transcribed Image Text:Explanation of Solution Given: The provided logarithmic function is y = In |sec a + tan z| Formula used: (F(9(z))) = f'(g(z)). g'(x) Calculation: Applying the Chain Rule, (|sec a + tan æ|)' y' sec z+ tan z sec z+tan z sec z+tan z| sOc z +tan z )(sec x tan x + sec² x) sec z+tan z| )(sec a + tan æ)' y' sec z+tan z| y' sec z+tan z| sec z+tan z (sec z tan z + sec? x) y' sec z+ tan z| (sec'z+tan z)(sec z tan z+sec?z) y' Isec z+ tan z? E Chapter 3.4, Problem 91E Chapter 3.4, Problem 93E → ||
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