Derivative of polynomial in GF(16)

Question

how can I find the derivative of the following polynomial in $GF(2^4)$: $\alpha x^4+x^3+\alpha x^2+\alpha^2 x+1$ ?

Answer 1

The derivative of the following polynomial: $\alpha x^4+x^3+\alpha x^2+\alpha^2 x+1$ in $GF(2^4)$ is:
$x^2+\alpha^2$.