Expert: Ahmed Salami - 8/23/2010

Question
I am working on alternating series questions. Here I need to solve derivative of Factorials such that
n
derivative of n!     derivative of (2n)! etc.

Please help me to solve these derivatives.


Thanks in Advance.

Answer
Hi Rashid,
Given that the factorial is a discrete function, not a continuous one, there is no continous derivative, so only the discrete derivative would be simple to formulate.
The factorial is only defined on the natural numbers, and there is no sensible way to take a derivative of any function on the naturals.

In that case where we want the discrete-space derivative,
d(x!)/dx = (x+1)! - x!
               = x.x!
               = x²(x-1)!

It might help more if I, perhaps, knew exactly what you were working on.

Regards