Cho hàm số f ( x ) = x ( x − 1 ) ( x − 2 ) . . . ( x − 1000 ) . Tính f′(0) ?

\[{\rm{f'}}\left( {\rm{0}} \right) = \mathop {\lim }\limits_{{\rm{x}} \to 0} \frac{{{\rm{f}}\left( {\rm{x}} \right) - {\rm{f}}\left( {\rm{0}} \right)}}{{{\rm{x}} - 0}} = \mathop {\lim }\limits_{{\rm{x}} \to 0} \frac{{{\rm{x}}\left( {{\rm{x}} - {\rm{1}}} \right)\left( {{\rm{x}} - {\rm{2}}} \right)...\left( {{\rm{x}} - {\rm{1000}}} \right) - {\rm{0}}}}{{\rm{x}}}\]

\[ = \mathop {\lim }\limits_{{\rm{x}} \to 0} \left( {{\rm{x}} - 1} \right)\left( {{\rm{x}} - 2} \right)...\left( {{\rm{x}} - 1000} \right) = \mathop {\lim }\limits_{{\rm{x}} \to 0} \left( { - 1} \right)\left( { - 2} \right)\left( { - 3} \right)...\left( { - 1000} \right) = {\left( { - 1} \right)^{1000}}.1000! = 1000!\]

Đáp án cần chọn là: B