> restart; # Berechnung der Ableitung von f mittels (f(x+h) -f(x))/h fuer h -> 0;
 ableitung:=proc(f,x)
 local i, h, res;
 h:=2;
 for i from 0 by 1 to 40 do 
    h:=h/2; 
    res:=(evalf(f(x+h)-f(x)))/h; 
    if irem(i,10)=0 then print(level=i, abstand=evalf(h), resultat=res)
  end if;       
  end do
  end proc;
 

> ableitung(cos, 1);
> 
       level = 0,  abstand = 1.,                 resultat = -0.9564491424
       level = 10, abstand = 0.0009765625000,    resultat = -0.8417342464
                                           -7                          
       level = 20, abstand = 9.536743164 10    , resultat = -0.8417968128
                                           -10                          
       level = 30, abstand = 9.313225746 10    , resultat = -0.9663676416
                                           -13               
       level = 40, abstand = 9.094947018 10   ,  resultat = 0.
>