Dear Dmitry,
you could later force the evaluation of the sum by ev(expr, simpsum).
result: factor(sum(diff(ev(expr,simpsum),a[j])*c[j],j,1,3));
%e^(a[3]*b[3]+a[2]*b[2]+a[1]*b[1])*(b[3]*c[3]+b[2]*c[2]+b[1]*c[1])
But I agree that it would be convenient, if maxima would be able to evaluate the differentiation, especially if the sum limits are not explicit.
Best regards,
Michael