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Question Number 123124 by aupo14 last updated on 23/Nov/20

Commented by Dwaipayan Shikari last updated on 23/Nov/20

$$x!=\mathrm{\Gamma }(x+1)$$$$log(x!)=log\left(\mathrm{\Gamma }(x+1)\right)$$$$\frac{\frac{dx!}{dx}}{x!}=\frac{{\mathrm{\Gamma }}^{\prime }(x+1)}{\mathrm{\Gamma }(x+1)}$$$$\Rightarrow \frac{d}{dx}(x!)=x!.\psi (x+1)$$$$$$

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