Derivative of the function $(x)!$.

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I had been learning calculus. So what I was thinking about is what us differentiation if $(x)!$. I know. 'n 'th derivative of $x^n$ is $x!$ but it isn''t helping me to solve this problem.

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Derivating $x!$ makes no sense since it is defined only for natural numbers, and therefore, it is not a continuous function, necessary condition to the existence of the derivative.