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Question Number 26947 by prakash jain last updated on 31/Dec/17

$$\frac{d}{dx}\ln \left(\mathrm{\Gamma }(x+1)\right)=?$$

Commented by abdo imad last updated on 31/Dec/17

$$weknowthat\mathrm{\Gamma }(x+1)=x\mathrm{\Gamma }\left(x\right)withx>0$$$$\Rightarrow ln\left(\mathrm{\Gamma }(x+1)\right)=lnx+ln\left(\mathrm{\Gamma }\left(x\right)\right)$$$$\Rightarrow \frac{d}{dx}ln\left(\mathrm{\Gamma }(x+1)\right)=\frac{1}{x}+\frac{{\mathrm{\Gamma }}^{,}\left(x\right)}{\mathrm{\Gamma }\left(x\right)}.$$

Answered by Femmy last updated on 31/Dec/17

$$\mathrm{ans}$$$$\ln \mathrm{\Gamma }+\ln (\mathrm{x}+1)$$$$1/\mathrm{\Gamma }+1/(\mathrm{x}+1)$$$$$$

Commented by prakash jain last updated on 31/Dec/17

$$\mathrm{Actually}\mathrm{I}\mathrm{meant}\mathrm{\Gamma }\mathrm{as}\mathrm{gamma}\mathrm{function}$$

Commented by Femmy last updated on 31/Dec/17

$$\mathrm{okay}\mathrm{sir}$$$$$$

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