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Let f(x)=(x-1)(x-2)(x-3)(x-n),n in N ,a...

Let `f(x)=(x-1)(x-2)(x-3)(x-n),n in N ,a n df(n)=5040.` Then the value of `n` is________

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In (f(x))=In (x-1)+In (x-2)+...+In (x-n)
`"or "f'(x)=f(x)[(1)/(x-1)+(1)/(x-2)+...(1)/(x-n)]`
`=(x-2)(x-3)(x-n)+(x-1)(x-3)...(x-n)+...+(x-1)(x-2)...(x-(n-1))`
`"or "f'(n)=(n-1)(n-2)(n-3)cdot3.2cdot1`
(all other factors except the last vanishes when x=n)
`"or "5040=(n-1)!`
`"or "n=8`
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