Question Number 123124 by aupo14 last updated on 23/Nov/20
Commented by Dwaipayan Shikari last updated on 23/Nov/20
$${x}!=\Gamma\left({x}+\mathrm{1}\right) \\ $$$${log}\left({x}!\right)={log}\left(\Gamma\left({x}+\mathrm{1}\right)\right) \\ $$$$\frac{\frac{{dx}!}{{dx}}}{{x}!}=\frac{\Gamma'\left({x}+\mathrm{1}\right)}{\Gamma\left({x}+\mathrm{1}\right)} \\ $$$$\Rightarrow\frac{{d}}{{dx}}\left({x}!\right)={x}!.\psi\left({x}+\mathrm{1}\right) \\ $$$$ \\ $$