Can the Derivative of a Summation be Calculated with a General Rule?

[Trepidation]

Hey,

I have a general question about summations. Is there any steadfast rule for calculating, or obtaining a sometimes-calculatable function for, the derivative of x, where x is the upper bound of summation in a simple summation expression (the summation of f(n), from n = 1 to x)?

If not, is there a general procedure that can be followed to obtain solutions to such problems?

Thanks,
-Trepidation

 

[mathman]

The upper bound of a sum is an integer, while x as the argument of a function (with a definable derivative) is a continuous variable. You need to define your problem better.