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.
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.
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)`
Find the derivative: