`y = cos((1 - e^(2x))/(1 + e^(2x)))` Find the derivative of the function.

Textbook Question

Chapter 3, 3.4 - Problem 35 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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growley52 | College Teacher | (Level 1) Adjunct Educator

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`d/(dy) [cos((1-e^(2x))/(1+e^(2x)))] = -sin((1-e^(2x))/(1+e^(2x)))[d/(dx) ((1-e^(2x))/(1+e^(2x)))]`

` ` `= -sin((1-e^(2x))/(1+e^(2x))){((1+e^(2x))(d/dx)(1-e^(2x)) - (1-e^(2x))(d/dx)(1+e^(2x)))/((1+e^(2x))^2)}`

`= -sin((1-e^(2x))/(1+e^(2x))){(-2e^(2x)(1-e^(2x))-2e^(2x)(1+e^(2x)))/((1+e^(2x))^2)}`

`= (4e^(2x)sin[(1-e^(2x))/(1+e^(2x))])/((1+e^(2x))^2)`

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