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

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Expert Answers

tiburtius | Certified Educator

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`

**Images:**

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