`f(x) = 1/(1 + e^(tan(x)))` Use a computer algebra system to graph `f` and to find `f'`

Textbook Question

Chapter 4, 4.6 - Problem 22 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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tiburtius | High School Teacher | (Level 2) Educator

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We will solve the problem using Wolfram Mathematica (you can also use Wolfram Alpha which is free).

Graph of 

Plot[1/(1 + E^Tan[x]), {x, - Pi/2, Pi/2}]

Plot[1/(1 + E^Tan[x]), {x, -6 Pi, 6 Pi}]

First line of code is used to make the first image and second to make the second image. The vertical lines in the second image are actually asymptotes.

Finding   

Simplify[D[1/(1 + E^Tan[x]), x]]

In the code line above command Simplify is there to simplify the result obtained by differentiation.

The result is `f'(x)=-(e^tan(x) sec^2(x))/(1 + e^tan(x))^2`

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