what is derivative of factorial of x ?

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)!