{"common":{"save":0,"post_id":"7121","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5905","post_id":"7121","mon_id":"1158924","chapter_id":"1159187","question":"<p>\u0110\u1ea1o hàm c\u1ee7a hàm s\u1ed1 <span class=\"math-tex\">$y=\\dfrac{x+3}{\\sqrt{x^2+1}}$<\/span> là:<\/p>","options":["<b>A.<\/b> <span class=\"math-tex\">$y^\\prime =\\dfrac{1-3x}{(x^2+1)\\sqrt{x^2+1}}$<\/span>","<b>B.<\/b> <span class=\"math-tex\">$y^\\prime =\\dfrac{1+3x}{(x^2+1)\\sqrt{x^2+1}}$<\/span>","<b>C.<\/b> <span class=\"math-tex\">$y^\\prime =\\dfrac{1-3x}{x^2+1}$<\/span>","<b>D.<\/b> <span class=\"math-tex\">$y^\\prime =\\dfrac{2x^2-x-1}{(x^2+1)\\sqrt{x^2+1}}$<\/span>"],"correct":"1","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><b>A.<\/b> <span class=\"math-tex\">$y^\\prime =\\dfrac{1-3x}{(x^2+1)\\sqrt{x^2+1}}$<\/span><\/span><\/p><p>Ta có: <span class=\"math-tex\">$y=\\dfrac{x+3}{\\sqrt{x^2+1}}$<\/span><\/p><p>⇒ <span class=\"math-tex\">$y^\\prime =\\dfrac{\\sqrt{x^2+1}-\\dfrac{(x+3)x}{\\sqrt{x^2+1}}}{(\\sqrt{x^2+1})^2} =\\dfrac{1-3x}{(x^2+1)\\sqrt{x^2+1}}$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-29 03:25:46","option_type":"math","len":0},{"id":"5907","post_id":"7121","mon_id":"1158924","chapter_id":"1159187","question":"<p>Cho <span class=\"math-tex\">$f (x)=\\sqrt{1-4x}+\\dfrac{1-x}{x-3}$<\/span>. Tính <span class=\"math-tex\">$f^\\prime (x)$<\/span>.<\/p>","options":["<b>A.<\/b> <span class=\"math-tex\">$f^\\prime (x)=\\dfrac{2}{\\sqrt{1-4x}}-\\dfrac{2}{x-3}$<\/span>","<b>B.<\/b> <span class=\"math-tex\">$f^\\prime (x)=\\dfrac{2}{\\sqrt{1-4x}}-\\dfrac{2}{(x-3)^2}$<\/span>","<b>C.<\/b> <span class=\"math-tex\">$f^\\prime (x)=\\dfrac{1}{2\\sqrt{1-4x}}+1$<\/span>","<b>D.<\/b> <span class=\"math-tex\">$f^\\prime (x)=\\dfrac{-2}{\\sqrt{1-4x}}+\\dfrac{2}{(x-3)^2}$<\/span>"],"correct":"4","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><b>D.<\/b> <span class=\"math-tex\">$f^\\prime (x)=\\dfrac{-2}{\\sqrt{1-4x}}+\\dfrac{2}{(x-3)^2}$<\/span><\/span><span style=\"color:#16a085;\"><\/span><\/p><p>Ta có: <span class=\"math-tex\">$f (x)=\\sqrt{1-4x}+\\dfrac{1-x}{x-3}$<\/span><\/p><p>⇒ <span class=\"math-tex\">$f^\\prime (x)=\\dfrac{-2}{\\sqrt{1-4x}}+\\dfrac{2}{(x-3)^2}$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-29 03:29:05","option_type":"math","len":0},{"id":"5909","post_id":"7121","mon_id":"1158924","chapter_id":"1159187","question":"<p>Cho hàm s\u1ed1 <span class=\"math-tex\">$y=x^3+mx^2+3x-5$<\/span> v\u1edbi m là tham s\u1ed1. Tìm t\u1eadp h\u1ee3p M g\u1ed3m t\u1ea5t c\u1ea3 các giá tr\u1ecb c\u1ee7a m \u0111\u1ec3 y' = 0 có hai nghi\u1ec7m phân bi\u1ec7t.<\/p>","options":["<b>A.<\/b> <span class=\"math-tex\">$M=(-3; 3)$<\/span>","<b>B.<\/b> <span class=\"math-tex\">$M=(-\\infty; -3]\\cup [3;+\\infty )$<\/span>","<b>C.<\/b> <span class=\"math-tex\">$M=\\mathbb{R}$<\/span>","<b>D.<\/b> <span class=\"math-tex\">$M=(-\\infty; -3)\\cup (3;+\\infty )$<\/span>"],"correct":"4","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><b>D.<\/b> <span class=\"math-tex\">$M=(-\\infty; -3)\\cup (3;+\\infty )$<\/span><\/span><\/p><p>Ta có: <span class=\"math-tex\">$y=x^3+mx^2+3x-5$<\/span> ⇒ <span class=\"math-tex\">$y^\\prime =3x^2+2mx+3$<\/span><\/p><p>Ph\u01b0\u01a1ng trình y' = 0 có hai nghi\u1ec7m phân bi\u1ec7t ⇔ <span class=\"math-tex\">$\\Delta^\\prime > 0$<\/span> ⇔ <span class=\"math-tex\">$m^2-9>0$<\/span> ⇔ <span class=\"math-tex\">$m\\in (-\\infty ;-3)\\cup (3;+\\infty )$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-05-29 03:39:44","option_type":"math","len":0}]}
