{"common":{"save":0,"post_id":"7117","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5873","post_id":"7117","mon_id":"1158924","chapter_id":"1159187","question":"<p>Cho hàm s\u1ed1 <span class=\"math-tex\">$y =\\dfrac{4}{x-1}$<\/span>. Khi \u0111ó <span class=\"math-tex\">$y^\\prime (-1)$<\/span> b\u1eb1ng<\/p>","options":["<b>A.<\/b> −1","<b>B.<\/b> −2","<b>C.<\/b> 1","<b>D.<\/b> 2"],"correct":"1","level":"1","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><b>A.<\/b> −1<\/span><\/p><p>Ta có: <span class=\"math-tex\">$y^\\prime =-\\dfrac{4}{(x-1)^2}$<\/span> ⇒ <span class=\"math-tex\">$y^\\prime (-1)=-1$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-29 01:22:33","option_type":"txt","len":1},{"id":"5874","post_id":"7117","mon_id":"1158924","chapter_id":"1159187","question":"<p>Tính \u0111\u1ea1o hàm c\u1ee7a hàm s\u1ed1 <span class=\"math-tex\">$f(x) =\\dfrac{2x+7}{x+4}$<\/span> t\u1ea1i x = 2 ta \u0111\u01b0\u1ee3c:<\/p>","options":["<b>A.<\/b> <span class=\"math-tex\">$f^\\prime(2)=\\dfrac{11}{6}$<\/span>","<b>B.<\/b> <span class=\"math-tex\">$f^\\prime(2)=\\dfrac{1}{36}$<\/span>","<b>C.<\/b> <span class=\"math-tex\">$f^\\prime(2)=\\dfrac{3}{2}$<\/span>","<b>D.<\/b> <span class=\"math-tex\">$f^\\prime(2)=\\dfrac{5}{12}$<\/span>"],"correct":"2","level":"1","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><b>B.<\/b> <span class=\"math-tex\">$f^\\prime(2)=\\dfrac{1}{36}$<\/span><\/span><\/p><p>Ta có: <span class=\"math-tex\">$f^\\prime(x) =\\dfrac{1}{(x+4)^2}$<\/span> ⇒ <span class=\"math-tex\">$f^\\prime(2)=\\dfrac{1}{36}$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-29 01:26:06","option_type":"math","len":0},{"id":"5876","post_id":"7117","mon_id":"1158924","chapter_id":"1159187","question":"<p>\u0110\u1ea1o hàm c\u1ee7a hàm s\u1ed1 y = x(x + 1)(x + 2)(x + 3) t\u1ea1i \u0111i\u1ec3m <span class=\"math-tex\">$x_0=0$<\/span> là:<\/p>","options":["<b>A.<\/b> y'(0) = 5","<b>B.<\/b> y'(0) = 6","<b>C.<\/b> y'(0) = 0","<b>D.<\/b> y'(0) = –6"],"correct":"2","level":"1","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><b>B.<\/b> y'(0) = 6<\/span><\/p><p>Ta có: <\/p><p><span class=\"math-tex\">$y = x(x + 1)(x + 2)(x + 3)=(x^2+x)(x^2+5x+6)=x^4+6x^3+11x^2+6x$<\/span><\/p><p>⇒ <span class=\"math-tex\">$y^\\prime =4x^3+18x^2+22x+6$<\/span><\/p><p>⇒ y'(0) = 6<\/p>","type":"choose","extra_type":"shape1","user_id":"131","test":"0","date":"2024-05-29 01:32:59","option_type":"txt","len":0}]}
