Differentiating sums



Hi,

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 <my sum>. 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).

Cheers,
Grzegorz