Example 7.  Use the Horner's method for higher derivatives to calculate all the derivatives    for the polynomial
        .  

Solution 7.

Enter the coefficients    of    in the first row of the matrix    and construct  .

Execute the subroutine loops for computing the entries in rows  2  through  n+2  of the matrix.

We can print out the values to see if they are correct.

The values     of the derivatives can be used to construct the Taylor polynomial of    expanded about  .

(c) John H. Mathews 2004