`f(theta) = sec(theta)/(1 + sec(theta))` Differentiate.

Textbook Question

Chapter 3, 3.3 - Problem 11 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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kspcr111 | In Training Educator

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`f(theta) = sec(theta)/(1 + sec(theta))`

so,

`f'(theta) = (sec(theta)/(1 + sec(theta)))'`

 `= (1- (1/(1 + sec(theta))))'`

  `= 0 -(1/(1 + sec(theta)))'`

  `= - tan(theta)* sec(theta)/(1 + sec(theta))^2`

` =- tan(theta)/((1 + sec(theta))^2* cos(theta))`

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