`f(x) = (x^2 - 1)e^(arctan(x))` Use a computer algebra system to graph `f` and to find `f'`

Expert Answers
tiburtius eNotes educator| Certified Educator

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

Graph of 

Plot[(x^2 - 1) E^ArcTan[x], {x, -3, 3}]

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

Finding   

Simplify[D[(x^2 - 1) E^ArcTan[x], x]]

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

The result is `e^arctan(x) (2 x + (-1 + x^2)/(1 + x^2))`

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scisser | Student

Graph

Find the derivative

`f'(x)=((x^2-1)/(x^2+1)+2x)e^(arctan(x))`