First of all, f(x)=x! where x is integer- is a group of dots on the plot. If you want to derivate such function like f(x)=x!, you should do it in complex numbers with Gamma function Г(z+1)=z! where Re(z)>0. Check it out on Wikipedia, it is interesting.

I would like to know if there is any method to make an estimation on how big it is a number, in terms of orders of magnitude of n! when n is a big number.

(x^2) (2-x)^2 = 1 + 2(2-x)^2 I asked this problem on this page a few months ago, but didn’t get any satisfactory answer. I think there is a trick solution to it

First of all, f(x)=x! where x is integer- is a group of dots on the plot. If you want to derivate such function like f(x)=x!, you should do it in complex numbers with Gamma function Г(z+1)=z! where Re(z)>0. Check it out on Wikipedia, it is interesting.