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

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tiburtius eNotes educator| Certified Educator

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

Graph of `f`    

Plot[(1 - E^(1/x))/(1 + E^(1/x)), {x, -5, 5}]

By writing the above line of code we obtain the image below. 

Finding `f'`  

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

Simplify is used to simplify the expression obtained by differentiation.

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

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