I need help in differentiating the following expression with respect to x, which I recently came up with when trying to differentiate expressions involving subfactorials...
$$(x!)\uparrow\uparrow(!x)$$
[Here, x $\in$ $\Bbb C$]
I would appreciate it, if the answerer could elaborate the method used to solve this problem; even a constructive hint would be excellent.
Note: Tetration, here, is quintessentially the next hyper operator after exponentiation. More details -> http://en.wikipedia.org/wiki/Tetration