{"id":530856,"date":"2026-03-16T15:41:44","date_gmt":"2026-03-16T08:41:44","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=530856"},"modified":"2026-03-16T15:41:44","modified_gmt":"2026-03-16T08:41:44","slug":"huong-dan-chi-tiet-dao-ham-cua-1-x-tu-a-den-z","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/huong-dan-chi-tiet-dao-ham-cua-1-x-tu-a-den-z\/","title":{"rendered":"H\u01b0\u1edbng D\u1eabn Chi Ti\u1ebft: \u0110\u1ea1o H\u00e0m C\u1ee7a 1\/x T\u1eeb A \u0110\u1ebfn Z"},"content":{"rendered":"<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">B\u00e0i vi\u1ebft n\u00e0y s\u1ebd cung c\u1ea5p m\u1ed9t c\u00e1i nh\u00ecn to\u00e0n di\u1ec7n v\u1ec1 <\/span><b>\u0111\u1ea1o h\u00e0m c\u1ee7a 1\/x<\/b><span style=\"font-weight: 400;\">, t\u1eeb nh\u1eefng kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n nh\u1ea5t, c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh to\u00e1n, \u0111\u1ebfn nh\u1eefng \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf v\u00e0 c\u00e1c tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t. Ch\u00fang ta s\u1ebd kh\u00e1m ph\u00e1 <\/span><span style=\"font-weight: 400;\">\u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 1\/x l\u00e0 g\u00ec<\/span><span style=\"font-weight: 400;\">, <\/span><span style=\"font-weight: 400;\">c\u00e1ch t\u00ednh \u0111\u1ea1o h\u00e0m 1\/x<\/span><span style=\"font-weight: 400;\"> m\u1ed9t c\u00e1ch chi ti\u1ebft, v\u00e0 ph\u00e2n bi\u1ec7t n\u00f3 v\u1edbi c\u00e1c kh\u00e1i ni\u1ec7m li\u00ean quan nh\u01b0 nguy\u00ean h\u00e0m.<\/span><\/p>\n<h2 style=\"text-align: justify;\"><b>\u0110\u1ea1o h\u00e0m c\u1ee7a 1\/x l\u00e0 g\u00ec?<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">\u0110\u1ea1o h\u00e0m c\u1ee7a m\u1ed9t h\u00e0m s\u1ed1 t\u1ea1i m\u1ed9t \u0111i\u1ec3m bi\u1ec3u th\u1ecb t\u1ed1c \u0111\u1ed9 bi\u1ebfn thi\u00ean t\u1ee9c th\u1eddi c\u1ee7a h\u00e0m s\u1ed1 \u0111\u00f3 t\u1ea1i \u0111i\u1ec3m \u0111\u00f3. Hi\u1ec3u \u0111\u01a1n gi\u1ea3n, \u0111\u1ea1o h\u00e0m cho bi\u1ebft h\u00e0m s\u1ed1 thay \u0111\u1ed5i nhanh\/ch\u1eadm th\u1ebf n\u00e0o khi bi\u1ebfn s\u1ed1 thay \u0111\u1ed5i m\u1ed9t l\u01b0\u1ee3ng r\u1ea5t nh\u1ecf. <\/span><span style=\"font-weight: 400;\">\u00dd ngh\u0129a trong h\u00ecnh h\u1ecdc c\u1ee7a<\/span><span style=\"font-weight: 400;\"> \u0111\u1ea1o h\u00e0m t\u1ea1i m\u1ed9t \u0111i\u1ec3m x<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\"> ch\u00ednh l\u00e0 h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a ti\u1ebfp tuy\u1ebfn v\u1edbi \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1 t\u1ea1i \u0111i\u1ec3m (x<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">, y<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">). V\u1edbi h\u00e0m s\u1ed1 <\/span><span style=\"font-weight: 400;\">y = 1\/x<\/span><span style=\"font-weight: 400;\">, \u0111\u1ea1o h\u00e0m m\u00f4 t\u1ea3 \u0111\u1ed9 nghi\u00eang c\u1ee7a ti\u1ebfp tuy\u1ebfn t\u1ea1i m\u1ed7i \u0111i\u1ec3m tr\u00ean \u0111\u1ed3 th\u1ecb.<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2026\/03\/dao-ham-cua-1-x-1.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2026\/03\/dao-ham-cua-1-x-1-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2026\/03\/dao-ham-cua-1-x-1-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-531048 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-1.jpg\" alt=\"dao-ham-cua-1-x-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Trong v\u1eadt l\u00fd, \u0111\u1ea1o h\u00e0m th\u01b0\u1eddng \u0111\u1ea1i di\u1ec7n cho v\u1eadn t\u1ed1c t\u1ee9c th\u1eddi, gia t\u1ed1c t\u1ee9c th\u1eddi ho\u1eb7c c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng thay \u0111\u1ed5i nhanh theo th\u1eddi gian. <\/span><span style=\"font-weight: 400;\">B\u00ean c\u1ea1nh \u0111\u00f3, mi\u1ec1n x\u00e1c \u0111\u1ecbnh c\u1ee7a<\/span><span style=\"font-weight: 400;\"> h\u00e0m s\u1ed1 <\/span><span style=\"font-weight: 400;\">y = 1\/x<\/span><span style=\"font-weight: 400;\"> x\u00e1c \u0111\u1ecbnh v\u1edbi m\u1ecdi x \u2260 0. T\u1ea1i x = 0, h\u00e0m s\u1ed1 kh\u00f4ng x\u00e1c \u0111\u1ecbnh v\u00e0 c\u0169ng kh\u00f4ng c\u00f3 \u0111\u1ea1o h\u00e0m.<\/span><\/p>\n<h2 style=\"text-align: justify;\"><b>C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u1ee7a 1\/x l\u00e0 g\u00ec?<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">H\u00e0m s\u1ed1 1\/x l\u00e0 m\u1ed9t d\u1ea1ng h\u00e0m s\u1ed1 \u0111\u01a1n gi\u1ea3n nh\u01b0ng l\u1ea1i xu\u1ea5t hi\u1ec7n kh\u00e1 nhi\u1ec1u trong c\u00e1c b\u00e0i to\u00e1n to\u00e1n h\u1ecdc v\u00e0 \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf. Vi\u1ec7c t\u00ecm hi\u1ec3u \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 n\u00e0y gi\u00fap ng\u01b0\u1eddi h\u1ecdc hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 c\u00e1ch h\u00e0m s\u1ed1 thay \u0111\u1ed5i theo bi\u1ebfn s\u1ed1, \u0111\u1ed3ng th\u1eddi t\u1ea1o n\u1ec1n t\u1ea3ng \u0111\u1ec3 ti\u1ebfp c\u1eadn v\u00e0 gi\u1ea3i quy\u1ebft c\u00e1c d\u1ea1ng b\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn \u0111\u1ea1o h\u00e0m \u1edf m\u1ee9c \u0111\u1ed9 cao h\u01a1n.<\/span><\/p>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\"><b>C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m:<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\">N\u1ebfu y = 1\/x \u21d2 y&#8217; = -1\/x<\/span><span style=\"font-weight: 400;\">2<\/span><\/li>\n<li style=\"font-weight: 400;\"><b>Ch\u1ee9ng minh b\u1eb1ng \u0111\u1ecbnh ngh\u0129a gi\u1edbi h\u1ea1n:<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\">Ta c\u00f3 \u0111\u1ecbnh ngh\u0129a \u0111\u1ea1o h\u00e0m t\u1ea1i x<\/span><span style=\"font-weight: 400;\">0<\/span><span style=\"font-weight: 400;\">:<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><b>f'(x<\/b><b>0<\/b><b>) = lim<\/b><b>h\u21920<\/b><b> [(f(x<\/b><b>0<\/b><b> + h) &#8211; f(x<\/b><b>0<\/b><b>))\/h]<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\">V\u1edbi f(x) = 1\/x:<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">f'(x) = lim<\/span><span style=\"font-weight: 400;\">h\u21920<\/span><span style=\"font-weight: 400;\"> [1\/(x + h) &#8211; 1\/x]\/h = lim<\/span><span style=\"font-weight: 400;\">h\u21920<\/span><span style=\"font-weight: 400;\"> [-h\/(x(x+h))]\/h = lim<\/span><span style=\"font-weight: 400;\">h\u21920<\/span><span style=\"font-weight: 400;\"> [-1\/(x(x+h))] = -1\/x<\/span><span style=\"font-weight: 400;\">2<\/span><\/li>\n<li style=\"font-weight: 400;\"><b>Ch\u1ee9ng minh b\u1eb1ng c\u00f4ng th\u1ee9c l\u0169y th\u1eeba:<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\">Vi\u1ebft l\u1ea1i 1\/x = x<\/span><span style=\"font-weight: 400;\">-1<\/span><span style=\"font-weight: 400;\">, \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m l\u0169y th\u1eeba:<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">N\u1ebfu y = x<\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\"> \u21d2 y&#8217; = n x<\/span><span style=\"font-weight: 400;\">n-1<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">V\u1edbi n = -1: y&#8217; = -1\u00b7x<\/span><span style=\"font-weight: 400;\">-2<\/span><span style=\"font-weight: 400;\"> = -1\/x<\/span><span style=\"font-weight: 400;\">2<\/span><\/li>\n<li style=\"font-weight: 400;\"><b>Gi\u1ea3i th\u00edch t\u1ea1i sao c\u00f3 d\u1ea5u \u00e2m:<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\">V\u00ec khi x t\u0103ng, gi\u00e1 tr\u1ecb 1\/x gi\u1ea3m, t\u1ed1c \u0111\u1ed9 gi\u1ea3m s\u1ebd ng\u00e0y c\u00e0ng nh\u1ecf l\u1ea1i v\u00e0 lu\u00f4n mang d\u1ea5u \u00e2m (h\u00e0m ngh\u1ecbch bi\u1ebfn tr\u00ean mi\u1ec1n x\u00e1c \u0111\u1ecbnh).<\/span><\/li>\n<\/ul>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2026\/03\/dao-ham-cua-1-x-2.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2026\/03\/dao-ham-cua-1-x-2-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2026\/03\/dao-ham-cua-1-x-2-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-531047 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-2.jpg\" alt=\"dao-ham-cua-1-x-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<h2 style=\"text-align: justify;\"><b>V\u00ed d\u1ee5 minh h\u1ecda c\u00e1ch t\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a 1\/x c\u01a1 b\u1ea3n<\/b><\/h2>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\"><b>B\u00e0i to\u00e1n:<\/b><span style=\"font-weight: 400;\"> T\u00ecm \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 y = 1\/x t\u1ea1i x = 2.<\/span><\/li>\n<li style=\"font-weight: 400;\"><b>L\u1eddi gi\u1ea3i:<\/b><span style=\"font-weight: 400;\"> Ta c\u00f3 y&#8217; = -1\/x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">. Thay x = 2 v\u00e0o: <\/span><span style=\"font-weight: 400;\">y'(2) = -1\/(2)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = -1\/4<\/span><\/li>\n<li style=\"font-weight: 400;\"><b>\u00dd ngh\u0129a k\u1ebft qu\u1ea3:<\/b><span style=\"font-weight: 400;\"> T\u1ea1i x = 2, h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a ti\u1ebfp tuy\u1ebfn \u0111\u1ed3 th\u1ecb y = 1\/x l\u00e0 -1\/4. \u0110i\u1ec1u n\u00e0y cho bi\u1ebft, n\u1ebfu x t\u0103ng l\u00ean m\u1ed9t ch\u00fat t\u1eeb 2, gi\u00e1 tr\u1ecb c\u1ee7a y s\u1ebd gi\u1ea3m v\u1edbi t\u1ed1c \u0111\u1ed9 g\u1ea7n -0,25 \u0111\u01a1n v\u1ecb tr\u00ean m\u1ed7i \u0111\u01a1n v\u1ecb x.<\/span><\/li>\n<li style=\"font-weight: 400;\"><b>V\u00ed d\u1ee5 kh\u00e1c:<\/b><span style=\"font-weight: 400;\"> T\u00ecm \u0111\u1ea1o h\u00e0m t\u1ea1i x = -3: <\/span><span style=\"font-weight: 400;\">y'(-3) = -1\/(-3)<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> = -1\/9<\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: justify;\"><b>C\u00e1c tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t v\u00e0 m\u1edf r\u1ed9ng c\u1ee7a \u0111\u1ea1o h\u00e0m 1\/x<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">T\u1eeb d\u1ea1ng h\u00e0m s\u1ed1 c\u01a1 b\u1ea3n ban \u0111\u1ea7u, c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c m\u1edf r\u1ed9ng khi h\u00e0m s\u1ed1 xu\u1ea5t hi\u1ec7n trong c\u00e1c bi\u1ec3u th\u1ee9c ph\u1ee9c t\u1ea1p h\u01a1n ho\u1eb7c k\u1ebft h\u1ee3p v\u1edbi nh\u1eefng ph\u00e9p bi\u1ebfn \u0111\u1ed5i \u0111\u1ea1i s\u1ed1 kh\u00e1c. Vi\u1ec7c t\u00ecm hi\u1ec3u c\u00e1c tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t n\u00e0y kh\u00f4ng ch\u1ec9 gi\u00fap c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c v\u1ec1 \u0111\u1ea1o h\u00e0m m\u00e0 c\u00f2n h\u1ed7 tr\u1ee3 ng\u01b0\u1eddi h\u1ecdc linh ho\u1ea1t h\u01a1n khi gi\u1ea3i c\u00e1c b\u00e0i to\u00e1n li\u00ean quan trong qu\u00e1 tr\u00ecnh h\u1ecdc t\u1eadp.<\/span><\/p>\n<h3 style=\"text-align: justify;\"><b>\u0110\u1ea1o h\u00e0m c\u1ee7a 1\/u (u l\u00e0 h\u00e0m s\u1ed1 theo x)<\/b><\/h3>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\"><b>C\u00f4ng th\u1ee9c:<\/b><span style=\"font-weight: 400;\"> N\u1ebfu y = 1\/u(x), th\u00ec y&#8217; = -u'(x)\/[u(x)]<\/span><span style=\"font-weight: 400;\">2<\/span><\/li>\n<li style=\"font-weight: 400;\"><b>V\u00ed d\u1ee5:<\/b><span style=\"font-weight: 400;\"> y = 1\/(2x+3)<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">u(x) = 2x+3 \u21d2 u'(x) = 2<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">y&#8217; = -2\/(2x+3)<\/span><span style=\"font-weight: 400;\">2<\/span><\/li>\n<\/ul>\n<h3 style=\"text-align: justify;\"><b>\u0110\u1ea1o h\u00e0m c\u1ee7a 1\/x<\/b><b>n<\/b><b> (x m\u0169 n)<\/b><\/h3>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\"><b>C\u00f4ng th\u1ee9c:<\/b><span style=\"font-weight: 400;\"> y = 1\/x<\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\"> \u21d2 y = x<\/span><span style=\"font-weight: 400;\">-n<\/span><span style=\"font-weight: 400;\">, v\u1eady y&#8217; = -n x<\/span><span style=\"font-weight: 400;\">-(n+1)<\/span><span style=\"font-weight: 400;\"> = -n\/x<\/span><span style=\"font-weight: 400;\">n+1<\/span><\/li>\n<li style=\"font-weight: 400;\"><b>V\u00ed d\u1ee5:<\/b><span style=\"font-weight: 400;\"> y = 1\/x<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\"> \u21d2 y&#8217; = -3\/x<\/span><span style=\"font-weight: 400;\">4<\/span><\/li>\n<\/ul>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2026\/03\/dao-ham-cua-1-x-3.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2026\/03\/dao-ham-cua-1-x-3-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2026\/03\/dao-ham-cua-1-x-3-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-531046 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-3.jpg\" alt=\"dao-ham-cua-1-x-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<h3 style=\"text-align: justify;\"><b>\u0110\u1ea1o h\u00e0m c\u1ee7a 1\/\u221ax, 1\/\u221au v\u00e0 c\u00e1c bi\u1ebfn th\u1ec3 c\u0103n th\u1ee9c<\/b><\/h3>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\"><b>C\u00f4ng th\u1ee9c t\u1ed5ng qu\u00e1t:<\/b><span style=\"font-weight: 400;\"> y = 1\/\u221ax = x<\/span><span style=\"font-weight: 400;\">-1\/2<\/span><span style=\"font-weight: 400;\"> \u21d2 y&#8217; = -1\/2 x<\/span><span style=\"font-weight: 400;\">-3\/2<\/span><span style=\"font-weight: 400;\"> = -1\/(2x\u221ax)<\/span><\/li>\n<li style=\"font-weight: 400;\"><b>V\u00ed d\u1ee5:<\/b><span style=\"font-weight: 400;\"> y = 1\/\u221a(2x)<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">u(x) = 2x \u21d2 u'(x) = 2<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">y&#8217; = -u'(x)\/[2u(x)\u221au(x)] = -2\/[2\u00b72x\u00b7\u221a(2x)] = -1\/(2x\u221a(2x))<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Ngo\u00e0i ra, \u0111\u1ea1o h\u00e0m c\u1ee7a 1\/2\u221ax l\u00e0:<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">y = 1\/(2\u221ax) \u21d2 y&#8217; = -1\/(4x\u221ax)<\/span><\/li>\n<\/ul>\n<h3 style=\"text-align: justify;\"><b>\u0110\u1ea1o h\u00e0m c\u1ea5p n c\u1ee7a 1\/x<\/b><\/h3>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">D\u00f9ng c\u00f4ng th\u1ee9c l\u0169y th\u1eeba v\u00e0 quy n\u1ea1p:<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">y = x<\/span><span style=\"font-weight: 400;\">-1<\/span><span style=\"font-weight: 400;\"> \u21d2 y&#8217;<\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\"> = (-1)<\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\">\u00b7n! \/ x<\/span><span style=\"font-weight: 400;\">n+1<\/span><\/li>\n<li style=\"font-weight: 400;\"><b>V\u00ed d\u1ee5:<\/b><span style=\"font-weight: 400;\"> \u0110\u1ea1o h\u00e0m c\u1ea5p 2 c\u1ee7a 1\/x l\u00e0:<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">y&#8221; = 2\/x<\/span><span style=\"font-weight: 400;\">3<\/span><\/li>\n<\/ul>\n<h3 style=\"text-align: justify;\"><b>B\u1ea3ng t\u1ed5ng h\u1ee3p \u0111\u1ea1o h\u00e0m c\u00e1c d\u1ea1ng 1\/x<\/b><\/h3>\n<table>\n<tbody>\n<tr>\n<td><b>D\u1ea1ng h\u00e0m s\u1ed1<\/b><\/td>\n<td><b>\u0110\u1ea1o h\u00e0m<\/b><\/td>\n<td><b>Ghi ch\u00fa<\/b><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">1\/x<\/span><\/td>\n<td><span style=\"font-weight: 400;\">-1\/x<\/span><span style=\"font-weight: 400;\">2<\/span><\/td>\n<td><span style=\"font-weight: 400;\">D\u1ea1ng c\u01a1 b\u1ea3n<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">1\/x<\/span><span style=\"font-weight: 400;\">n<\/span><\/td>\n<td><span style=\"font-weight: 400;\">-n\/x<\/span><span style=\"font-weight: 400;\">n+1<\/span><\/td>\n<td><span style=\"font-weight: 400;\">n \u2208 \u211d, n \u2260 0<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">1\/u(x)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">-u'(x)\/[u(x)]<\/span><span style=\"font-weight: 400;\">2<\/span><\/td>\n<td><span style=\"font-weight: 400;\">u(x) l\u00e0 h\u00e0m b\u1ea5t k\u1ef3 theo x<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">1\/\u221ax<\/span><\/td>\n<td><span style=\"font-weight: 400;\">-1\/(2x\u221ax)<\/span><\/td>\n<td><span style=\"font-weight: 400;\">x &gt; 0<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 style=\"text-align: justify;\"><b>Nguy\u00ean h\u00e0m v\u00e0 c\u00e1c kh\u00e1i ni\u1ec7m li\u00ean quan \u0111\u1ebfn \u0111\u1ea1o h\u00e0m c\u1ee7a 1\/x<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Khi t\u00ecm hi\u1ec3u v\u1ec1 \u0111\u1ea1o h\u00e0m c\u1ee7a m\u1ed9t h\u00e0m s\u1ed1, vi\u1ec7c xem x\u00e9t nguy\u00ean h\u00e0m v\u00e0 c\u00e1c kh\u00e1i ni\u1ec7m li\u00ean quan s\u1ebd gi\u00fap m\u1edf r\u1ed9ng g\u00f3c nh\u00ecn, \u0111\u1ed3ng th\u1eddi l\u00e0m r\u00f5 c\u00e1ch c\u00e1c ph\u00e9p to\u00e1n vi ph\u00e2n v\u00e0 t\u00edch ph\u00e2n li\u00ean k\u1ebft v\u1edbi nhau. Nh\u1edd \u0111\u00f3, ng\u01b0\u1eddi h\u1ecdc c\u00f3 th\u1ec3 n\u1eafm v\u1eefng b\u1ea3n ch\u1ea5t c\u1ee7a h\u00e0m s\u1ed1 v\u00e0 \u00e1p d\u1ee5ng linh ho\u1ea1t v\u00e0o nhi\u1ec1u d\u1ea1ng b\u00e0i to\u00e1n kh\u00e1c nhau trong qu\u00e1 tr\u00ecnh h\u1ecdc to\u00e1n.<\/span><\/p>\n<h3 style=\"text-align: justify;\"><b>Nguy\u00ean h\u00e0m c\u1ee7a 1\/x<\/b><\/h3>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\"><b>C\u00f4ng th\u1ee9c nguy\u00ean h\u00e0m:<\/b><span style=\"font-weight: 400;\"> \u222b1\/x dx = ln|x| + C<\/span><\/li>\n<li style=\"font-weight: 400;\"><b>\u00dd ngh\u0129a:<\/b><span style=\"font-weight: 400;\"> N\u1ebfu b\u1ea1n l\u1ea5y \u0111\u1ea1o h\u00e0m c\u1ee7a ln|x|, b\u1ea1n s\u1ebd thu \u0111\u01b0\u1ee3c l\u1ea1i 1\/x. \u0110i\u1ec1u n\u00e0y th\u1ec3 hi\u1ec7n t\u00ednh \u0111\u1ed1i ng\u1eabu gi\u1eefa \u0111\u1ea1o h\u00e0m v\u00e0 nguy\u00ean h\u00e0m.<\/span><\/li>\n<\/ul>\n<h3 style=\"text-align: justify;\"><b>C\u00e1c d\u1ea1ng nguy\u00ean h\u00e0m li\u00ean quan<\/b><\/h3>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\"><b>Nguy\u00ean h\u00e0m c\u1ee7a 1\/x<\/b><b>n<\/b><b> (n \u2260 1):<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\">\u222b1\/x<\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\"> dx = 1\/(1-n)\u00b7x<\/span><span style=\"font-weight: 400;\">1-n<\/span><span style=\"font-weight: 400;\"> + C<\/span><\/li>\n<li style=\"font-weight: 400;\"><b>Nguy\u00ean h\u00e0m c\u1ee7a 1\/\u221ax:<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\">\u222b1\/\u221ax dx = 2\u221ax + C<\/span><\/li>\n<li style=\"font-weight: 400;\"><b>Nguy\u00ean h\u00e0m c\u1ee7a 1\/x<\/b><b>3<\/b><b>:<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\">\u222b1\/x<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\"> dx = -1\/(2x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">) + C<\/span><\/li>\n<li style=\"font-weight: 400;\"><b>Nguy\u00ean h\u00e0m c\u1ee7a 1\/x<\/b><b>5<\/b><b>:<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\">\u222b1\/x<\/span><span style=\"font-weight: 400;\">5<\/span><span style=\"font-weight: 400;\"> dx = -1\/(4x<\/span><span style=\"font-weight: 400;\">4<\/span><span style=\"font-weight: 400;\">) + C<\/span><\/li>\n<\/ul>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2026\/03\/dao-ham-cua-1-x-4.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2026\/03\/dao-ham-cua-1-x-4-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2026\/03\/dao-ham-cua-1-x-4-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-531045 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-4.jpg\" alt=\"dao-ham-cua-1-x-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<h3 style=\"text-align: justify;\"><b>Ph\u00e2n bi\u1ec7t \u0111\u1ea1o h\u00e0m v\u00e0 nguy\u00ean h\u00e0m c\u1ee7a 1\/x<\/b><\/h3>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\"><b>\u0110\u1ea1o h\u00e0m:<\/b><span style=\"font-weight: 400;\"> &#8220;\u0110\u1ecdc t\u1ed1c \u0111\u1ed9 thay \u0111\u1ed5i&#8221; \u2013 cho bi\u1ebft h\u00e0m 1\/x bi\u1ebfn thi\u00ean nh\u01b0 th\u1ebf n\u00e0o t\u1ea1i t\u1eebng \u0111i\u1ec3m.<\/span><\/li>\n<li style=\"font-weight: 400;\"><b>Nguy\u00ean h\u00e0m:<\/b><span style=\"font-weight: 400;\"> &#8220;\u0110\u1ecdc di\u1ec7n t\u00edch d\u01b0\u1edbi \u0111\u01b0\u1eddng cong&#8221; \u2013 cho bi\u1ebft t\u00edch l\u0169y c\u1ee7a h\u00e0m s\u1ed1 1\/x tr\u00ean m\u1ed9t kho\u1ea3ng.<\/span><\/li>\n<\/ul>\n<h3 style=\"text-align: justify;\"><b>B\u00e0i t\u1eadp v\u00ed d\u1ee5<\/b><\/h3>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\"><b>B\u00e0i 1:<\/b><span style=\"font-weight: 400;\"> T\u00ednh \u222b1\/x dx t\u1eeb x = 1 \u0111\u1ebfn x = 4.<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><b>L\u1eddi gi\u1ea3i:<\/b><span style=\"font-weight: 400;\"> ln|4| &#8211; ln|1| = ln4<\/span><\/li>\n<li style=\"font-weight: 400;\"><b>B\u00e0i 2:<\/b><span style=\"font-weight: 400;\"> T\u00ecm nguy\u00ean h\u00e0m c\u1ee7a 1\/x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">.<\/span><span style=\"font-weight: 400;\"><br \/>\n<\/span><span style=\"font-weight: 400;\">\u222b1\/x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\"> dx = \u222bx<\/span><span style=\"font-weight: 400;\">-2<\/span><span style=\"font-weight: 400;\"> dx = -x<\/span><span style=\"font-weight: 400;\">-1<\/span><span style=\"font-weight: 400;\"> + C = -1\/x + C<\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: justify;\"><b>\u1ee8ng d\u1ee5ng v\u00e0 \u0111i\u1ec1u ki\u1ec7n c\u1ee7a \u0111\u1ea1o h\u00e0m 1\/x trong th\u1ef1c t\u1ebf<\/b><\/h2>\n<p style=\"text-align: justify;\"><span style=\"font-weight: 400;\">Kh\u00f4ng ch\u1ec9 d\u1eebng l\u1ea1i \u1edf l\u00fd thuy\u1ebft, \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 1\/x c\u00f2n \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 ph\u00e2n t\u00edch s\u1ef1 thay \u0111\u1ed5i c\u1ee7a c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau. B\u00ean c\u1ea1nh \u0111\u00f3, vi\u1ec7c n\u1eafm \u0111\u01b0\u1ee3c c\u00e1c \u0111i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh v\u00e0 ph\u1ea1m vi \u00e1p d\u1ee5ng c\u1ee7a \u0111\u1ea1o h\u00e0m c\u0169ng gi\u00fap ng\u01b0\u1eddi h\u1ecdc s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c m\u1ed9t c\u00e1ch ch\u00ednh x\u00e1c v\u00e0 hi\u1ec7u qu\u1ea3 khi gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n li\u00ean quan.<\/span><\/p>\n<h3 style=\"text-align: justify;\"><b>\u0110i\u1ec1u ki\u1ec7n \u00e1p d\u1ee5ng \u0111\u1ea1o h\u00e0m c\u1ee7a 1\/x<\/b><\/h3>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">H\u00e0m s\u1ed1 1\/x ch\u1ec9 c\u00f3 \u0111\u1ea1o h\u00e0m t\u1ea1i m\u1ecdi x \u2260 0. T\u1ea1i x = 0, h\u00e0m s\u1ed1 kh\u00f4ng x\u00e1c \u0111\u1ecbnh n\u00ean kh\u00f4ng c\u00f3 \u0111\u1ea1o h\u00e0m.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Khi \u00e1p d\u1ee5ng cho c\u00e1c h\u00e0m h\u1ee3p, \u0111i\u1ec1u ki\u1ec7n x\u00e1c \u0111\u1ecbnh ph\u1ea3i l\u00e0 u(x) \u2260 0.<\/span><\/li>\n<\/ul>\n<h3 style=\"text-align: justify;\"><b>\u1ee8ng d\u1ee5ng trong v\u1eadt l\u00fd<\/b><\/h3>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">M\u1ed1i quan h\u1ec7 gi\u1eefa v\u1eadn t\u1ed1c v\u00e0 th\u1eddi gian khi qu\u00e3ng \u0111\u01b0\u1eddng l\u00e0 m\u1ed9t h\u00e0m t\u1ec9 l\u1ec7 ngh\u1ecbch v\u1edbi th\u1eddi gian.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">M\u00f4 h\u00ecnh ph\u00e2n r\u00e3 ph\u00f3ng x\u1ea1, \u0111i\u1ec7n tr\u1edf, c\u01b0\u1eddng \u0111\u1ed9 d\u00f2ng \u0111i\u1ec7n trong m\u1ea1ch \u0111i\u1ec7n&#8230; \u0111\u1ec1u c\u00f3 s\u1eed d\u1ee5ng \u0111\u1ea1o h\u00e0m 1\/x khi m\u00f4 t\u1ea3 bi\u1ebfn thi\u00ean ngh\u1ecbch \u0111\u1ea3o.<\/span><\/li>\n<\/ul>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2026\/03\/dao-ham-cua-1-x-5.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2026\/03\/dao-ham-cua-1-x-5-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2026\/03\/dao-ham-cua-1-x-5-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-531044 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-5.jpg\" alt=\"dao-ham-cua-1-x-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/03\/dao-ham-cua-1-x-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<h3 style=\"text-align: justify;\"><b>\u1ee8ng d\u1ee5ng trong kinh t\u1ebf h\u1ecdc<\/b><\/h3>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">H\u00e0m s\u1ea3n l\u01b0\u1ee3ng bi\u00ean gi\u1ea3m d\u1ea7n, chi ph\u00ed trung b\u00ecnh, hi\u1ec7u qu\u1ea3 c\u1eadn bi\u00ean&#8230; th\u01b0\u1eddng c\u00f3 d\u1ea1ng h\u00e0m s\u1ed1 ngh\u1ecbch \u0111\u1ea3o.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u0110\u1ea1o h\u00e0m 1\/x cho bi\u1ebft t\u1ed1c \u0111\u1ed9 thay \u0111\u1ed5i l\u1ee3i nhu\u1eadn, chi ph\u00ed ho\u1eb7c c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng kinh t\u1ebf kh\u00e1c trong nhi\u1ec1u b\u00e0i to\u00e1n th\u1ef1c t\u1ebf.<\/span><\/li>\n<\/ul>\n<h3 style=\"text-align: justify;\"><b>\u1ee8ng d\u1ee5ng trong to\u00e1n h\u1ecdc v\u00e0 k\u1ef9 thu\u1eadt<\/b><\/h3>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">S\u1eed d\u1ee5ng trong b\u00e0i to\u00e1n c\u1ef1c tr\u1ecb, kh\u1ea3o s\u00e1t h\u00e0m s\u1ed1, gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh vi ph\u00e2n, t\u00edch ph\u00e2n.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Gi\u1ea3i th\u00edch \u00fd ngh\u0129a c\u1ee7a t\u1ed1c \u0111\u1ed9 gi\u1ea3m d\u1ea7n, \u0111\u1ed9 cong c\u1ee7a \u0111\u1ed3 th\u1ecb, c\u00e1c \u0111\u1eb7c tr\u01b0ng h\u00ecnh h\u1ecdc kh\u00e1c c\u1ee7a h\u00e0m s\u1ed1.<\/span><\/li>\n<\/ul>\n<h3 style=\"text-align: justify;\"><b>M\u1edf r\u1ed9ng sang c\u00e1c h\u00e0m ph\u1ee9c t\u1ea1p h\u01a1n<\/b><\/h3>\n<ul style=\"text-align: justify;\">\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u0110\u1ea1o h\u00e0m 1\/x v\u1edbi c\u00e1c h\u00e0m s\u1ed1 kh\u00e1c (v\u00ed d\u1ee5: 1\/sin x, 1\/cos x, 1\/|x|, 1\/u(x)&#8230;)<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">V\u1eadn d\u1ee5ng quy t\u1eafc \u0111\u1ea1o h\u00e0m ri\u00eang bi\u1ec7t cho t\u1eebng tr\u01b0\u1eddng h\u1ee3p, k\u1ebft h\u1ee3p \u0111\u1ea1o h\u00e0m h\u00e0m h\u1ee3p, \u0111\u1ea1o h\u00e0m t\u00edch, \u0111\u1ea1o h\u00e0m th\u01b0\u01a1ng&#8230;<\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: justify;\"><b>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p<\/b><\/h2>\n<p style=\"text-align: justify;\"><b>\u0110\u1ea1o h\u00e0m c\u1ee7a 1\/x b\u1eb1ng bao nhi\u00eau?<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\">\u0110\u1ea1o h\u00e0m 1\/x l\u00e0 -1\/x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">. \u0110\u00e2y l\u00e0 m\u1ed9t trong nh\u1eefng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u01a1 b\u1ea3n nh\u1ea5t m\u00e0 b\u1ea1n c\u1ea7n ghi nh\u1edb khi h\u1ecdc gi\u1ea3i t\u00edch v\u00e0 \u00e1p d\u1ee5ng v\u00e0o c\u00e1c b\u00e0i to\u00e1n th\u1ef1c t\u1ebf.<\/span><\/p>\n<p style=\"text-align: justify;\"><b>\u0110\u1ea1o h\u00e0m c\u1ee7a 1\/u(x) l\u00e0 g\u00ec?<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\">N\u1ebfu u = u(x) l\u00e0 m\u1ed9t h\u00e0m s\u1ed1 kh\u1ea3 vi, th\u00ec \u0111\u1ea1o h\u00e0m c\u1ee7a 1\/u(x) l\u00e0 -u'(x)\/[u(x)]<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">. \u0110\u00e2y l\u00e0 tr\u01b0\u1eddng h\u1ee3p t\u1ed5ng qu\u00e1t h\u00f3a c\u1ee7a \u0111\u1ea1o h\u00e0m 1\/x.<\/span><\/p>\n<p style=\"text-align: justify;\"><b>\u0110\u1ea1o h\u00e0m 1\/x x\u00e1c \u0111\u1ecbnh t\u1ea1i x = 0 kh\u00f4ng?<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\">Kh\u00f4ng, v\u00ec t\u1ea1i x = 0 h\u00e0m s\u1ed1 1\/x kh\u00f4ng x\u00e1c \u0111\u1ecbnh, do \u0111\u00f3 \u0111\u1ea1o h\u00e0m c\u0169ng kh\u00f4ng t\u1ed3n t\u1ea1i \u1edf \u0111i\u1ec3m n\u00e0y.<\/span><\/p>\n<p style=\"text-align: justify;\"><b>\u0110\u1ea1o h\u00e0m 1\/x<\/b><b>n<\/b><b> l\u00e0 g\u00ec?<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\">\u0110\u1ea1o h\u00e0m 1\/x<\/span><span style=\"font-weight: 400;\">n<\/span><span style=\"font-weight: 400;\"> l\u00e0 -n\/x<\/span><span style=\"font-weight: 400;\">n+1<\/span><span style=\"font-weight: 400;\">, \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c l\u0169y th\u1eeba cho x<\/span><span style=\"font-weight: 400;\">-n<\/span><span style=\"font-weight: 400;\">.<\/span><\/p>\n<p style=\"text-align: justify;\"><b>\u1ee8ng d\u1ee5ng th\u1ef1c t\u1ebf c\u1ee7a \u0111\u1ea1o h\u00e0m 1\/x l\u00e0 g\u00ec?<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\">\u0110\u1ea1o h\u00e0m 1\/x \u0111\u01b0\u1ee3c d\u00f9ng trong v\u1eadt l\u00fd (t\u1ed1c \u0111\u1ed9 ngh\u1ecbch \u0111\u1ea3o, \u0111i\u1ec7n tr\u1edf, ph\u00e2n r\u00e3), kinh t\u1ebf (chi ph\u00ed trung b\u00ecnh, s\u1ea3n l\u01b0\u1ee3ng bi\u00ean), k\u1ef9 thu\u1eadt (t\u00ednh to\u00e1n t\u1ed1c \u0111\u1ed9 thay \u0111\u1ed5i t\u1ec9 l\u1ec7 ngh\u1ecbch) v\u00e0 nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c.<\/span><\/p>\n<p style=\"text-align: justify;\"><b>\u0110\u1ea1o h\u00e0m c\u1ea5p 2 c\u1ee7a 1\/x l\u00e0 g\u00ec?<\/b><b><br \/>\n<\/b><span style=\"font-weight: 400;\">\u0110\u1ea1o h\u00e0m c\u1ea5p 2 c\u1ee7a 1\/x l\u00e0 2\/x<\/span><span style=\"font-weight: 400;\">3<\/span><span style=\"font-weight: 400;\">, t\u00ednh b\u1eb1ng c\u00e1ch l\u1ea5y \u0111\u1ea1o h\u00e0m l\u1ea7n n\u1eefa c\u1ee7a -1\/x<\/span><span style=\"font-weight: 400;\">2<\/span><span style=\"font-weight: 400;\">.<\/span><\/p>\n<p><strong>Xem th\u00eam:<\/strong><\/p>\n<ul>\n<li>\n<p class=\"elementor-heading-title elementor-size-default\"><span style=\"color: #339966;\"><strong><a style=\"color: #339966;\" href=\"https:\/\/hoanghamobile.com\/tin-tuc\/tai-phan-mem-geogebra\/\">GeoGebra \u2013 Ph\u1ea7n m\u1ec1m v\u1ebd \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1, c\u00f4ng th\u1ee9c To\u00e1n h\u1ecdc<\/a><\/strong><\/span><\/p>\n<\/li>\n<li>\n<p class=\"elementor-heading-title elementor-size-default\"><span style=\"color: #339966;\"><strong><a style=\"color: #339966;\" href=\"https:\/\/hoanghamobile.com\/tin-tuc\/tai-mathtype\/\">Download MathType \u2013 Ph\u1ea7n m\u1ec1m so\u1ea1n th\u1ea3o c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc<\/a><\/strong><\/span><\/p>\n<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>B\u00e0i vi\u1ebft n\u00e0y s\u1ebd cung c\u1ea5p m\u1ed9t c\u00e1i nh\u00ecn to\u00e0n di\u1ec7n v\u1ec1 \u0111\u1ea1o h\u00e0m c\u1ee7a 1\/x, t\u1eeb nh\u1eefng kh\u00e1i ni\u1ec7m c\u01a1 b\u1ea3n nh\u1ea5t, c\u00e1c c\u00f4ng th\u1ee9c t\u00ednh to\u00e1n, \u0111\u1ebfn nh\u1eefng \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf v\u00e0 c\u00e1c tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t. 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