Tính đạo hàm của hàm số

\[f\left( x \right) = x\left( {x - 1} \right)\left( {x - 2} \right)...\left( {x - 2018} \right)\]

\[\begin{array}{*{20}{l}}{ \Rightarrow f'\left( x \right) = 1.\left( {x - 1} \right)\left( {x - 2} \right)...\left( {x - 2018} \right) + x.1.\left( {x - 2} \right)...\left( {x - 2018} \right) + x\left( {x - 1} \right).1.\left( {x - 2} \right)...\left( {x - 2018} \right) + ... + }\\{x.\left( {x - 1} \right)\left( {x - 2} \right)...\left( {x - 2017} \right).1}\end{array}\]\[ \Rightarrow f'\left( 0 \right) = 1.\left( { - 1} \right)\left( { - 2} \right)...\left( { - 2018} \right) + 0 + 0 + ... + 0 = 1.2...2018.{( - 1)^{2018}} = 2018!\]