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Question Number 202255 by SANOGO last updated on 23/Dec/23
calcul f_n ′(x)  f_n (x)=n^α x(1−x)^(n )
$${calcul}\:{f}_{{n}} '\left({x}\right) \\ $$$${f}_{{n}} \left({x}\right)={n}^{\alpha} {x}\left(\mathrm{1}−{x}\right)^{{n}\:} \: \\ $$
Answered by SANOGO last updated on 23/Dec/23
calculer la derivee de cette suite de fonction
$${calculer}\:{la}\:{derivee}\:{de}\:{cette}\:{suite}\:{de}\:{fonction} \\ $$
Answered by elcogito last updated on 24/Dec/23
f′_n (x)=n^α ((1−x)^n +nx(1−x)^(n−1) )              =n^α (1−x)^(n−1) ((n−1)x+1)
$${f}'_{{n}} \left({x}\right)={n}^{\alpha} \left(\left(\mathrm{1}−{x}\right)^{{n}} +{nx}\left(\mathrm{1}−{x}\right)^{{n}−\mathrm{1}} \right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:={n}^{\alpha} \left(\mathrm{1}−{x}\right)^{{n}−\mathrm{1}} \left(\left({n}−\mathrm{1}\right){x}+\mathrm{1}\right) \\ $$$$ \\ $$

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