GAP Manual: 19.10. Derivative

Derivative( f )

Let f be a Laurent polynomial (..., f_(-1), f_0, f_1, ...). Then Derivative returns the polynomial g = (..., g_(i-1) = i* f_i, ... ).

    gap> x := Indeterminate(Rationals);; x.name := "x";;
    gap> Derivative( x^10 + x^-11 );
    10*x^9 - 11*x^(-12)
    gap> y := Indeterminate(GF(5));; y.name := "y";;    
    gap> Derivative( y^10 + y^-11 );
    Z(5)^2*y^(-12)