Differentiating sums with Maxima

Question

I have the following sum:

sum((R[i]-(a*X[i]+b)*t + 1/2*(c*X[i]+d)^2*t)^2/((c*X[i]+d)^2*t), i, 1, N);

which I want to differenciate wrt. a:

diff(%, a);

but Maxima (wxMaxima to be precise) just prints d/da . Can I make it actually differentiate the sum (so because N is finite is should differentiate every element in the sum separately)?

If I set N to some constant, e.g.:

sum((R[i]-(a*X[i]+b)*t + 1/2*(c*X[i]+d)^2*t)^2/((c*X[i]+d)^2*t), i, 1, 100);

then I get explicit sum of 100 elements (takes about 2 pages), and then differentiation works (but again I get 2 pages instead of a small sum). Can I get this result displayed as a sum?

Answer 1

Which version of Maxima do you use ?

Here is my session of Maxima with you equation differentiated wrt.a and than substituted to N=100.

~$ maxima 
Maxima 5.24.0 http://maxima.sourceforge.net
using Lisp SBCL 1.0.51
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) sum((R[i]-(a*X[i]+b)*t + 1/2*(c*X[i]+d)^2*t)^2/((c*X[i]+d)^2*t), i, 1, N);
                                   2
                         (c X  + d)  t
                   N         i                             2
                  ====  (------------- - (a X  + b) t + R )
                  \            2             i           i
                   >    ------------------------------------
                  /                           2                                                                                                
                  ====              (c X  + d)                                                                                                 
                  i = 1                 i                                                                                                      
(%o1)             ------------------------------------------                                                                                   
                                      t                                                                                                        
(%i2) diff(%, a);                                                                                                                              
                                       2                                                                                                       
                             (c X  + d)  t                                                                                                     
                    N            i
                   ====  X  (------------- - (a X  + b) t + R )
                   \      i        2             i           i
(%o2)          - 2  >    --------------------------------------
                   /                            2
                   ====               (c X  + d)
                   i = 1                  i
(%i3) %, N=100;
                                       2
                             (c X  + d)  t
                   100           i
                   ====  X  (------------- - (a X  + b) t + R )
                   \      i        2             i           i
(%o3)          - 2  >    --------------------------------------
                   /                            2
                   ====               (c X  + d)
                   i = 1                  i