This is the table we constructed in class for center-difference approximations of f' (0) for the exponential function.

difflist = 
      Table[h = 10. ^-n; {Exp[h], 
          Exp[-h], (Exp[h] - Exp[-h])/2/h}, {n, 1, 16, 
          1}]

TableForm[difflist]

We can used PaddedForm to get a uniform formatting of numbers.  Below, {17,16} means PaddedForm will display 17 digits with 16 of them to the right of the decimal.

PaddedForm[difflist // TableForm, {17, 16}]

The next set of inputs just sets things up to work more generally.  You can define the function and the point at which the derivative is to be approximated.

f[x_] = Cos[x];
x0 = 1;
difflist = 
        Table[h = 10. ^-n; {f[x0 + h], 
            f[x0 - h], (f[x0 + h] - f[x0 - h])/2/h}, {n, 1, 16, 
            1}];
PaddedForm[TableForm[difflist], {17, 16}]