Cho hàm số (y = dfrac{{{x^2}}}{{1 – x}}). Đạo hàm cấp 2018 của hàm số (fleft( x right)) là:

Ta có:

(begin{array}{l}fleft( x right) = dfrac{{{x^2}}}{{1 – x}} = dfrac{{{x^2} – 1 + 1}}{{1 – x}} =  – x – 1 + dfrac{1}{{1 – x}}\ Rightarrow f’left( x right) =  – 1 + dfrac{1}{{{{left( {x – 1} right)}^2}}}\,,,,,,f”left( x right) = dfrac{{ – 2left( {x – 1} right)}}{{{{left( {x – 1} right)}^4}}} = dfrac{{ – 2}}{{{{left( {x – 1} right)}^3}}}\,,,,,f”’left( x right) = dfrac{{2.3{{left( {x – 1} right)}^2}}}{{{{left( {x – 1} right)}^6}}} = dfrac{{2.3}}{{{{left( {x – 1} right)}^4}}}\…….\ Rightarrow {f^{left( {2018} right)}}left( x right) = dfrac{{ – 2.3…2018}}{{{{left( {x – 1} right)}^{2019}}}} =  – dfrac{{2018!}}{{{{left( {x – 1} right)}^{2019}}}} = dfrac{{2018!}}{{{{left( {1 – x} right)}^{2019}}}}end{array})

Chọn B.