how do you take a derivative of a factorial? For example,
1/n!
?
2007-04-08 05:31:45 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
The factorial is a special case of the gamma function. The gamma function is defined as (this is gonna be ugly since I can't type math symbols here):
Gamma(z) = Integral over t from 0 to infinity of [t^(z-1) exp(-t)]dt
...which is a continuous, differentiable function. If z is an integer then you get the factorial. See http://rkb.home.cern.ch/rkb/AN16pp/node96.html
Also, see http://www.sosmath.com/calculus/improper/gamma/gamma.html which actually gives you the derivative.
2007-04-08 05:42:15 · answer #1 · answered by Astronomer1980 3 · 0⤊ 0⤋
The derivative applies to continuos functions and n! is only defined at your level at natural integers.
In higher calculus you´ll define a function(gamma function of a continuos variable x )which for x=n gives you n!)
2007-04-08 07:28:38 · answer #2 · answered by santmann2002 7 · 0⤊ 0⤋
You can't, because the factorial function is not continuous, it is not differentiable. The factorial function is only defined for whole numbers.
2007-04-08 05:34:35 · answer #3 · answered by Anonymous · 4⤊ 1⤋
The function is not continuous and only defined for integers so you can't.
2007-04-08 08:27:40 · answer #4 · answered by sweet_angel92 3 · 0⤊ 0⤋
you can't
2007-04-08 05:44:09 · answer #5 · answered by Melissa 2 · 1⤊ 0⤋