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Question Number 70891 by Henri Boucatchou last updated on 09/Oct/19

$$\mathit{f}\left(\mathit{x}\right)=\mathit{x}(\mathit{x}-1)(\mathit{x}-2)....(\mathit{x}-10)$$$$\mathit{f}{}^{\prime }\left(0\right)=?$$

Commented by kaivan.ahmadi last updated on 09/Oct/19

$$letg\left(x\right)=(x-1)(x-2)...(x-10)\Rightarrow f\left(x\right)=xg\left(x\right)$$$$\Rightarrow f^{\prime }\left(x\right)=g\left(x\right)+{xg}^{\prime }\left(x\right)\Rightarrow$$$$f^{\prime }\left(0\right)=g\left(0\right)+0=g\left(0\right)=(-1)(-2)...(-10)=10!$$

Commented by Prithwish sen last updated on 09/Oct/19

$$\mathrm{Excellent}\mathrm{Sir}.$$

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