`f(x) = (x^(2/3))/(1 + x + x^4)` Use a computer algebra system to graph `f` and to find `f'`

Expert Answers
tiburtius eNotes educator| Certified Educator

We will find the derivative using Wolfram Mathematica (you can also use Wolfram Alpha which is free). For graphing we will use GeoGebra (freeware) because Mathematica cannot graph powers with fractional exponents for negative numbers.

Graph of 

f(x)=x^(2 / 3) / (1 + x + x^4)

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

Finding   

Simplify[D[x^(2/3)/(1 + x + x^4), x]]

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

The result is `f'(x)=(2 - x - 10 x^4)/(3 x^(1/3) (1 + x + x^4)^2)`

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scisser | Student

Graph

Find the derivative:

`f'(x)=(-10x^4-x+2)/(3*root(3)x(x^4+x+1)^2))`