Question

Is it possible to differentiate a factorial? if yes, how?

Answer 1

use the general form of x factorial to figure it out.

Answer 2

The derivative of x factorial exists, therefore it is possible to differentiate a factorial.

Answer 3

in differentiating (k-1)!...

Answer 4

...according to wolframalpha

Answer 5

It's this problem that has been bugging for quite a time... I have no Idea how to differentiate...

d/dx ( (-1)^(k-1) (k-1)!/(x^k)

Answer 6

Someone is claiming that it is not possible to differentiate a factorial because it creates a contradiction with the definition of a derivative. He says the value of h approaching zero in the limit, assumes that the function is defined everywhere in a very close neighborhood to a particular value of x. And that since factorials are restricted to being defined by whole numbers, which are discrete and not continuous, finding the derivative of a factorial is not possible.

Answer 7

if k is restricted to being a positive integer, is getting it's derivative possible?

Answer 8

Even if you restricted k to positive numbers, that won't change the fact that factorials are discrete. The definition of a derivative requires that the function be continuous along an interval. And well, with factorials having discrete, non-continuous components, an interval doesn't exist.

Answer 9

oh, so that means we won't be able to get the derivative of the earlier equation...

Someone, solved it earlier but i just didn't get how he ended up with this. Would you please explain it to me?

d/dx ( (-1)^(k-1) (k-1)!/(x^k) ) = (-1)^(k-1) (k-1)! (-k)/(x^(k+1))

Answer 10

The derivative is taken with respect to x, not k

Answer 11

k is assumed to be constant in this case.

Answer 12

ooh. now I get it. Thanks for your help @Hero . All those explanations really helped me.. Thanks again..

Answer 13

You're welcome :)

Answer 14

there has to be a limit and lhl = rhs which we don't have with discrete.