{"id":297756,"date":"2023-12-25T16:27:34","date_gmt":"2023-12-25T09:27:34","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=297756"},"modified":"2025-12-20T15:40:03","modified_gmt":"2025-12-20T08:40:03","slug":"cong-thuc-dao-ham","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/","title":{"rendered":"\u0110\u1ea1o h\u00e0m sin: C\u00f4ng th\u1ee9c, ch\u1ee9ng minh v\u00e0 b\u00e0i t\u1eadp l\u01b0\u1ee3ng gi\u00e1c \u0111\u1ea7y \u0111\u1ee7"},"content":{"rendered":"<p><span style=\"font-weight: 400;\">\u0110\u1ea1o h\u00e0m sin l\u00e0 c\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n l\u1edbp 11: (sin x)&#8217; = cos x. B\u00e0i vi\u1ebft h\u01b0\u1edbng d\u1eabn chi ti\u1ebft ch\u1ee9ng minh b\u1eb1ng \u0111\u1ecbnh ngh\u0129a \u0111\u1ea1o h\u00e0m, b\u1ea3ng \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7 c\u00e1c h\u00e0m l\u01b0\u1ee3ng gi\u00e1c (sin, cos, tan, cot\u2026), b\u00e0i t\u1eadp t\u00ednh \u0111\u1ea1o h\u00e0m sin u v\u00e0 \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf trong v\u1eadt l\u00fd, kinh t\u1ebf. Xem ngay \u0111\u1ec3 n\u1eafm v\u1eefng!<\/span><\/p>\n<h2><b>\u0110\u1ea1o h\u00e0m sin l\u00e0 g\u00ec? C\u00f4ng th\u1ee9c v\u00e0 ch\u1ee9ng minh<\/b><\/h2>\n<p><span style=\"font-weight: 400;\">\u0110\u1ea1o h\u00e0m sin x = cos x, t\u1ed3n t\u1ea1i v\u1edbi m\u1ecdi x th\u1ef1c.<\/span><\/p>\n<p><b>B\u1ea3ng \u0111\u1ea1o h\u00e0m h\u00e0m l\u01b0\u1ee3ng gi\u00e1c c\u01a1 b\u1ea3n (l\u1edbp 11):<\/b><\/p>\n<table>\n<thead>\n<tr>\n<th><span style=\"font-weight: 400;\">H\u00e0m s\u1ed1<\/span><\/th>\n<th><span style=\"font-weight: 400;\">\u0110\u1ea1o h\u00e0m<\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00a0<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><span style=\"font-weight: 400;\">sin x<\/span><\/td>\n<td><span style=\"font-weight: 400;\">cos x<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">cos x<\/span><\/td>\n<td><span style=\"font-weight: 400;\">-sin x<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">tan x<\/span><\/td>\n<td><span style=\"font-weight: 400;\">1\/cos\u00b2 x (sec\u00b2 x)<\/span><\/td>\n<\/tr>\n<tr>\n<td><span style=\"font-weight: 400;\">cot x<\/span><\/td>\n<td><span style=\"font-weight: 400;\">-1\/sin\u00b2 x (-csc\u00b2 x)<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><b>Ch\u1ee9ng minh \u0111\u1ea1o h\u00e0m sin x b\u1eb1ng \u0111\u1ecbnh ngh\u0129a:<\/b><\/p>\n<p><span style=\"font-weight: 400;\">(sin x)&#8217; = lim_{h\u21920} [sin(x+h) &#8211; sin x]\/h = lim [2 cos((2x+h)\/2) sin(h\/2)] \/ h = cos x (s\u1eed d\u1ee5ng lim sin h\/h =1 v\u00e0 lim (cos h -1)\/h=0).<\/span><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-1.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-1-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-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-298356 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-1.jpg\" alt=\" cong-thuc-dao-ham-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p>C\u00f4ng th\u1ee9c c\u1ee7a \u0111\u1ea1o h\u00e0m c\u01a1 b\u1ea3n c\u1ee7a m\u1ed9t s\u1ed1 h\u00e0m s\u1ed1 ph\u1ed5 bi\u1ebfn nh\u01b0 sau:<\/p>\n<ul>\n<li>\u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 h\u1eb1ng: f(x) = c, v\u1edbi c l\u00e0 m\u1ed9t h\u1eb1ng s\u1ed1, \u0111\u1ea1o h\u00e0m c\u1ee7a f(x) l\u00e0 f'(x) = 0.<\/li>\n<li>\u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 m\u0169: f(x) = x^n, v\u1edbi n l\u00e0 m\u1ed9t s\u1ed1 nguy\u00ean d\u01b0\u01a1ng, \u0111\u1ea1o h\u00e0m c\u1ee7a f(x) l\u00e0 f'(x) = nx^(n-1).<\/li>\n<li>\u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 m\u0169 t\u1ef1 nhi\u00ean: f(x) = e^x, \u0111\u1ea1o h\u00e0m c\u1ee7a f(x) l\u00e0 f'(x) = e^x.<\/li>\n<li>\u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 sin v\u00e0 cos: f(x) = sin(x), f'(x) = cos(x); f(x) = cos(x), f'(x) = -sin(x).<\/li>\n<\/ul>\n<p>Ngo\u00e0i ra, c\u00f2n c\u00f3 nhi\u1ec1u c\u00f4ng th\u1ee9c v\u1ec1 \u0111\u1ea1o h\u00e0m kh\u00e1c cho c\u00e1c lo\u1ea1i h\u00e0m s\u1ed1 kh\u00e1c nhau nh\u01b0 h\u00e0m s\u1ed1 h\u1ee3p, h\u00e0m s\u1ed1 m\u0169, h\u00e0m s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c, h\u00e0m s\u1ed1 m\u0169, v\u00e0 nhi\u1ec1u lo\u1ea1i h\u00e0m s\u1ed1 ph\u1ee9c t\u1ea1p kh\u00e1c.<\/p>\n<h2>\u00dd ngh\u0129a c\u1ee7a c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m<\/h2>\n<p>Trong l\u0129nh v\u1ef1c v\u1eadt l\u00fd, c\u00f4ng th\u1ee9c c\u1ee7a \u0111\u1ea1o h\u00e0m \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ednh to\u00e1n v\u1eadn t\u1ed1c, gia t\u1ed1c v\u00e0 c\u00e1c \u0111\u1ea1i l\u01b0\u1ee3ng kh\u00e1c trong qu\u00e1 tr\u00ecnh di chuy\u1ec3n c\u1ee7a v\u1eadt th\u1ec3. \u0110\u1ea1o h\u00e0m cho bi\u1ebft t\u1ed1c \u0111\u1ed9 thay \u0111\u1ed5i c\u1ee7a m\u1ed9t h\u00e0m s\u1ed1 t\u1ea1i m\u1ed7i \u0111i\u1ec3m. \u0110i\u1ec1u n\u00e0y r\u1ea5t h\u1eefu \u00edch trong vi\u1ec7c hi\u1ec3u s\u1ef1 bi\u1ebfn \u0111\u1ed5i c\u1ee7a c\u00e1c hi\u1ec7n t\u01b0\u1ee3ng trong th\u1ebf gi\u1edbi th\u1ef1c. T\u1eeb t\u1ed1c \u0111\u1ed9 di chuy\u1ec3n c\u1ee7a v\u1eadt th\u1ec3 \u0111\u1ebfn t\u1ed1c \u0111\u1ed9 t\u0103ng tr\u01b0\u1edfng c\u1ee7a d\u00e2n s\u1ed1 hay t\u1ed1c \u0111\u1ed9 thay \u0111\u1ed5i c\u1ee7a gi\u00e1 c\u1ea3.<\/p>\n<p>Trong kinh t\u1ebf h\u1ecdc, \u0111\u1ea1o h\u00e0m \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u1ed1i \u01b0u h\u00f3a h\u00e0m l\u1ee3i nhu\u1eadn v\u00e0 t\u00ecm ra \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i ho\u1eb7c c\u1ef1c ti\u1ec3u c\u1ee7a h\u00e0m s\u1ed1. C\u00f4ng th\u1ee9c c\u1ee7a \u0111\u1ea1o h\u00e0m \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong t\u1ed1i \u01b0u h\u00f3a, n\u01a1i m\u00e0 ch\u00fang ta c\u1ed1 g\u1eafng t\u00ecm ra gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t ho\u1eb7c nh\u1ecf nh\u1ea5t c\u1ee7a m\u1ed9t h\u00e0m s\u1ed1. B\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng \u0111\u1ea1o h\u00e0m, ch\u00fang ta c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh c\u00e1c \u0111i\u1ec3m c\u1ef1c tr\u1ecb v\u00e0 \u0111i\u1ec3m u\u1ed1n c\u1ee7a h\u00e0m s\u1ed1. T\u1eeb \u0111\u00f3 gi\u00fap t\u1ed1i \u01b0u h\u00f3a c\u00e1c v\u1ea5n \u0111\u1ec1 th\u1ef1c t\u1ebf nh\u01b0 t\u1ed1i \u01b0u h\u00f3a chi ph\u00ed, t\u1ed1i \u01b0u h\u00f3a hi\u1ec7u su\u1ea5t, v.v.<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-5.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-5-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-5-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-298352 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-5.jpg\" alt=\" cong-thuc-dao-ham-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p>\u0110\u1ea1o h\u00e0m c\u00f2n gi\u00fap ch\u00fang ta hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 t\u00ednh ch\u1ea5t c\u1ee7a h\u00e0m s\u1ed1, bao g\u1ed3m \u0111\u1ed3 th\u1ecb, \u0111i\u1ec3m c\u1ef1c tr\u1ecb, \u0111i\u1ec3m u\u1ed1n, v\u00e0 xu h\u01b0\u1edbng t\u0103ng ho\u1eb7c gi\u1ea3m c\u1ee7a h\u00e0m s\u1ed1.<\/p>\n<p>\u0110\u1ea1o h\u00e0m \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong c\u00e1c l\u0129nh v\u1ef1c khoa h\u1ecdc v\u00e0 k\u1ef9 thu\u1eadt nh\u01b0 v\u1eadt l\u00fd, k\u1ef9 thu\u1eadt \u0111i\u1ec7n, k\u1ef9 thu\u1eadt h\u00f3a h\u1ecdc, khoa h\u1ecdc m\u00e1y t\u00ednh, kinh t\u1ebf h\u1ecdc, v.v.<\/p>\n<h2>C\u00e1c c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m<\/h2>\n<p>Sau khi hi\u1ec3u r\u00f5 \u0111\u01b0\u1ee3c \u00fd ngh\u0129a c\u1ee7a \u0111\u1ea1o h\u00e0m l\u00e0 g\u00ec. Ch\u00fang ta s\u1ebd \u0111i \u0111\u1ebfn ph\u1ea7n c\u00f4ng th\u1ee9c c\u1ee7a c\u00e1c lo\u1ea1i \u0111\u1ea1o h\u00e0m nh\u00e9.<\/p>\n<p><strong>C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m s\u01a1 c\u1ea5p<\/strong><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-2.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-2-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-2-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img decoding=\"async\" class=\"aligncenter size-full wp-image-298355 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-2.jpg\" alt=\" cong-thuc-dao-ham-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><strong>C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u1ea5p cao<\/strong><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-3.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-3-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-3-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298354 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-3.jpg\" alt=\" cong-thuc-dao-ham-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><strong>C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m l\u01b0\u1ee3ng gi\u00e1c<\/strong><\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-4.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-4-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-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-298353 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-4.jpg\" alt=\" cong-thuc-dao-ham-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p>Nh\u1edb r\u1eb1ng, c\u00f3 nhi\u1ec1u quy t\u1eafc kh\u00e1c nhau, ch\u1eb3ng h\u1ea1n nh\u01b0 quy t\u1eafc chu\u1ed7i, quy t\u1eafc nh\u00e2n, v\u00e0 quy t\u1eafc chia, \u0111\u1ec3 t\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a c\u00e1c h\u00e0m ph\u1ee9c t\u1ea1p h\u01a1n.<\/p>\n<h2>V\u00ed d\u1ee5 c\u00e1ch t\u00ednh \u0111\u1ea1o h\u00e0m<\/h2>\n<p>C\u00f3 nhi\u1ec1u ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ec3 t\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a m\u1ed9t h\u00e0m s\u1ed1. M\u1ed7i ph\u01b0\u01a1ng ph\u00e1p c\u00f3 c\u00e1ch \u00e1p d\u1ee5ng ri\u00eang. V\u00e0 ch\u00fang ta s\u1ebd \u0111i s\u00e2u v\u00e0o t\u1eebng ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ec3 gi\u00fap c\u00e1c b\u1ea1n hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 c\u00e1ch t\u00ednh \u0111\u1ea1o h\u00e0m.<\/p>\n<h3>C\u00e1ch t\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 m\u0169<\/h3>\n<p>H\u00e0m s\u1ed1 m\u0169 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n d\u01b0\u1edbi d\u1ea1ng f(x) = a^x, v\u1edbi a l\u00e0 m\u1ed9t h\u1eb1ng s\u1ed1 d\u01b0\u01a1ng. \u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 m\u0169 \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng c\u00f4ng th\u1ee9c sau: <strong>f'(x) = a^x * ln(a)<\/strong>.<\/p>\n<p>Trong \u0111\u00f3, ln(a) l\u00e0 logarit t\u1ef1 nhi\u00ean c\u1ee7a a. V\u00ed d\u1ee5, \u0111\u1ec3 t\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 f(x) = 2^x, ta \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c tr\u00ean v\u00e0 c\u00f3: <strong>f'(x) = 2^x * ln(2)<\/strong>.<\/p>\n<h3>C\u00e1ch t\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 logarit<\/h3>\n<p>H\u00e0m s\u1ed1 logarit t\u1ef1 nhi\u00ean \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n d\u01b0\u1edbi d\u1ea1ng f(x) = ln(x). C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 logarit \u0111\u01b0\u1ee3c t\u00ednh nh\u01b0 sau: f'(x) = 1\/x<\/p>\n<p>V\u00ed d\u1ee5, \u0111\u1ec3 t\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 f(x) = ln(x), ta \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c tr\u00ean v\u00e0 c\u00f3: <strong>f'(x) = 1\/x<\/strong><\/p>\n<p><strong><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-11.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-11-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-11-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298361 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-11.jpg\" alt=\"cong-thuc-dao-ham-11\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-11.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-11-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-11-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/strong><\/p>\n<p>H\u00e0m s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c c\u00f3 th\u1ec3 l\u00e0 sin(x), cos(x), ho\u1eb7c tan(x). \u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 sin(x) v\u00e0 cos(x) \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng c\u00f4ng th\u1ee9c sau:<strong> f'(x) = cos(x) (n\u1ebfu f(x) = sin(x)) f'(x) = -sin(x) (n\u1ebfu f(x) = cos(x))<\/strong><\/p>\n<p>\u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 tan(x) \u0111\u01b0\u1ee3c t\u00ednh nh\u01b0 sau: <strong>f'(x) = sec^2(x)<\/strong><\/p>\n<p>Trong \u0111\u00f3, sec(x) l\u00e0 h\u00e0m s\u1ed1 secant, \u0111\u01b0\u1ee3c \u0111\u1ecbnh ngh\u0129a l\u00e0 sec(x) = 1\/cos(x). V\u00ed d\u1ee5, \u0111\u1ec3 t\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 f(x) = sin(x), ta \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c tr\u00ean v\u00e0 c\u00f3: <strong>f'(x) = cos(x)<\/strong><\/p>\n<h3>C\u00e1ch t\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 h\u1ee3p<\/h3>\n<p>H\u00e0m s\u1ed1 h\u1ee3p l\u00e0 h\u00e0m s\u1ed1 \u0111\u01b0\u1ee3c t\u1ea1o th\u00e0nh b\u1eb1ng c\u00e1ch k\u1ebft h\u1ee3p c\u00e1c h\u00e0m s\u1ed1 kh\u00e1c v\u1edbi nhau. \u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 h\u1ee3p \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng quy t\u1eafc chu\u1ed7i (chain rule). Quy t\u1eafc chu\u1ed7i n\u00f3i r\u1eb1ng \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 h\u1ee3p f(g(x)) \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng t\u00edch gi\u1eefa \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 ngo\u00e0i f v\u00e0 \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 trong g.<\/p>\n<p>V\u00ed d\u1ee5, \u0111\u1ec3 t\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 f(x) = sin(2x), ta \u00e1p d\u1ee5ng quy t\u1eafc chu\u1ed7i v\u00e0 c\u00f3: <strong>f'(x) = cos(2x) * 2<\/strong><\/p>\n<p>Trong \u0111\u00f3, c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 ngo\u00e0i f l\u00e0 cos(x), v\u00e0 \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 trong g l\u00e0 2x (v\u00ec g(x) = 2x). Do \u0111\u00f3, t\u00edch gi\u1eefa hai \u0111\u1ea1o h\u00e0m n\u00e0y l\u00e0 cos(2x) * 2.<\/p>\n<p><strong><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-10.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-10-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-10-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298359 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-10.jpg\" alt=\"cong-thuc-dao-ham-10\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-10.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-10-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-10-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/strong><\/p>\n<p>Nh\u01b0 v\u1eady, qua c\u00e1c v\u00ed d\u1ee5 tr\u00ean, ch\u00fang ta \u0111\u00e3 th\u1ea5y \u0111\u01b0\u1ee3c c\u00e1ch t\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 ph\u1ed5 bi\u1ebfn v\u00e0 c\u00e1ch \u00e1p d\u1ee5ng ch\u00fang trong th\u1ef1c t\u1ebf. Vi\u1ec7c hi\u1ec3u r\u00f5 v\u1ec1 \u0111\u1ea1o h\u00e0m v\u00e0 c\u00e1ch \u00e1p d\u1ee5ng ch\u00fang s\u1ebd gi\u00fap ch\u00fang ta gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn t\u1ed1c \u0111\u1ed9, gia t\u1ed1c, t\u1ed1i \u01b0u h\u00f3a v\u00e0 nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c.<\/p>\n<h2>Minh h\u1ecda v\u1ec1 c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m<\/h2>\n<p>\u0110\u1ec3 b\u1ea1n c\u00f3 th\u1ec3 h\u00ecnh dung \u0111\u01b0\u1ee3c \u0111\u1ea1o h\u00e0m d\u00f9ng \u0111\u1ec3 l\u00e0m g\u00ec c\u0169ng nh\u01b0 \u0111\u1ea1o h\u00e0m \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng ra sao. C\u00f9ng m\u00ecnh \u0111\u1ecdc h\u1ebft m\u1ee5c n\u00e0y \u0111\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n nh\u00e9.<\/p>\n<p><strong>T\u00ednh t\u1ed1c \u0111\u1ed9 v\u00e0 gia t\u1ed1c<\/strong><\/p>\n<p>Trong v\u1eadt l\u00fd, \u0111\u1ea1o h\u00e0m \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ednh to\u00e1n t\u1ed1c \u0111\u1ed9 v\u00e0 gia t\u1ed1c c\u1ee7a v\u1eadt th\u1ec3. T\u1ed1c \u0111\u1ed9 c\u1ee7a m\u1ed9t v\u1eadt th\u1ec3 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1eb1ng \u0111\u1ea1o h\u00e0m c\u1ee7a v\u1ecb tr\u00ed theo th\u1eddi gian. Trong khi gia t\u1ed1c c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng \u0111\u1ea1o h\u00e0m c\u1ee7a t\u1ed1c \u0111\u1ed9 theo th\u1eddi gian.<\/p>\n<p><strong>V\u00ed d\u1ee5<\/strong>: N\u1ebfu v\u1ecb tr\u00ed c\u1ee7a m\u1ed9t v\u1eadt th\u1ec3 \u0111\u01b0\u1ee3c m\u00f4 t\u1ea3 b\u1edfi h\u00e0m s\u1ed1 s(t) = 5t^2 &#8211; 3t + 2. Th\u00ec v\u1eadn t\u1ed1c c\u1ee7a v\u1eadt th\u1ec3 t\u1ea1i th\u1eddi \u0111i\u1ec3m t=a c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh b\u1eb1ng \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 s(t) t\u1ea1i t=a, t\u1ee9c l\u00e0 s'(a).<\/p>\n<p><strong><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-7.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-7-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-7-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298357 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-7.jpg\" alt=\"ong-thuc-dao-ham-7\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-7.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-7-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-7-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/strong><\/p>\n<p>M\u1ed9t v\u00ed d\u1ee5 c\u1ee5 th\u1ec3 v\u1ec1 vi\u1ec7c \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m l\u00e0 trong v\u1eadt l\u00fd. Khi m\u1ed9t v\u1eadt th\u1ec3 di chuy\u1ec3n theo m\u1ed9t \u0111\u01b0\u1eddng cong. Ch\u00fang ta c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng \u0111\u1ea1o h\u00e0m \u0111\u1ec3 t\u00ednh to\u00e1n v\u1eadn t\u1ed1c c\u1ee7a v\u1eadt th\u1ec3 t\u1ea1i m\u1ed9t th\u1eddi \u0111i\u1ec3m c\u1ee5 th\u1ec3. V\u1eadn t\u1ed1c c\u1ee7a v\u1eadt th\u1ec3 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1eb1ng \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 v\u1ecb tr\u00ed theo th\u1eddi gian.<\/p>\n<p><strong>T\u1ed1i \u01b0u ho\u00e1<\/strong><\/p>\n<p>Trong kinh t\u1ebf h\u1ecdc v\u00e0 k\u1ef9 thu\u1eadt, \u0111\u1ea1o h\u00e0m \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u1ed1i \u01b0u h\u00f3a c\u00e1c h\u00e0m m\u1ee5c ti\u00eau. B\u1eb1ng c\u00e1ch t\u00ecm \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m m\u1ee5c ti\u00eau v\u00e0 \u0111\u1eb7t n\u00f3 b\u1eb1ng 0, ch\u00fang ta c\u00f3 th\u1ec3 t\u00ecm ra gi\u00e1 tr\u1ecb t\u1ed1i \u01b0u c\u1ee7a bi\u1ebfn s\u1ed1.<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-6.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-6-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-6-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298351 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-6.jpg\" alt=\" cong-thuc-dao-ham-6\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-6-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-6-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p>Ch\u00fang ta s\u1ebd cung c\u1ea5p m\u1ed9t s\u1ed1 v\u00ed d\u1ee5 c\u1ee5 th\u1ec3 v\u1ec1 c\u00e1ch t\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 ph\u1ed5 bi\u1ebfn. Nh\u01b0 h\u00e0m s\u1ed1 m\u0169, h\u00e0m s\u1ed1 logarit, h\u00e0m s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c, v\u00e0 h\u00e0m s\u1ed1 h\u1ee3p.<\/p>\n<h2>M\u00f4 ph\u1ecfng c\u00e1c t\u00ecnh hu\u1ed1ng th\u1ef1c t\u1ebf b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng \u0111\u1ea1o h\u00e0m<\/h2>\n<p>M\u00f4 ph\u1ecfng c\u00e1c t\u00ecnh hu\u1ed1ng th\u1ef1c t\u1ebf b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng \u0111\u1ea1o h\u00e0m l\u00e0 m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p quan tr\u1ecdng \u0111\u1ec3 hi\u1ec3u v\u00e0 gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau.<\/p>\n<p><strong>V\u1edbi chuy\u1ec3n \u0111\u1ed9ng v\u00e0 v\u1eadn t\u1ed1c<\/strong><\/p>\n<p>Gi\u1ea3 s\u1eed ch\u00fang ta mu\u1ed1n m\u00f4 ph\u1ecfng chuy\u1ec3n \u0111\u1ed9ng c\u1ee7a m\u1ed9t v\u1eadt th\u1ec3 d\u1ef1a tr\u00ean h\u00e0m v\u1ecb tr\u00ed theo th\u1eddi gian. B\u1eb1ng c\u00e1ch l\u1ea5y \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m v\u1ecb tr\u00ed \u0111\u00f3. Ch\u00fang ta c\u00f3 th\u1ec3 t\u00ednh \u0111\u01b0\u1ee3c v\u1eadn t\u1ed1c c\u1ee7a v\u1eadt th\u1ec3 t\u1ea1i m\u1ecdi th\u1eddi \u0111i\u1ec3m.<\/p>\n<p><strong>T\u1ed1i \u01b0u h\u00f3a chi ph\u00ed s\u1ea3n xu\u1ea5t<\/strong><\/p>\n<p>Trong k\u1ef9 thu\u1eadt v\u00e0 qu\u1ea3n l\u00fd s\u1ea3n xu\u1ea5t, vi\u1ec7c t\u1ed1i \u01b0u h\u00f3a chi ph\u00ed l\u00e0 quan tr\u1ecdng. C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ecm ra gi\u00e1 tr\u1ecb c\u1ef1c ti\u1ec3u c\u1ee7a h\u00e0m chi ph\u00ed, gi\u00fap t\u1ed1i \u01b0u h\u00f3a quy tr\u00ecnh s\u1ea3n xu\u1ea5t.<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-12.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-12-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-12-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298363 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-12.jpg\" alt=\"cong-thuc-dao-ham-13\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-12.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-12-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-12-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><strong>D\u1ef1 \u0111o\u00e1n xu h\u01b0\u1edbng t\u00e0i ch\u00ednh<\/strong><\/p>\n<p>\u0110\u1ea1o h\u00e0m c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 m\u00f4 ph\u1ecfng bi\u1ebfn \u0111\u1ed9ng c\u1ee7a gi\u00e1 c\u1ed5 phi\u1ebfu. Vi\u1ec7c n\u00e0y gi\u00fap d\u1ef1 \u0111o\u00e1n xu h\u01b0\u1edbng th\u1ecb tr\u01b0\u1eddng v\u00e0 h\u1ed7 tr\u1ee3 quy\u1ebft \u0111\u1ecbnh giao d\u1ecbch.<\/p>\n<p><strong>T\u1ed1i \u01b0u h\u00f3a m\u1ea1ng neuron trong Machine Learning<\/strong><\/p>\n<p>Trong deep learning, vi\u1ec7c c\u1eadp nh\u1eadt tr\u1ecdng s\u1ed1 c\u1ee7a m\u1ea1ng neuron d\u1ef1a tr\u00ean \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m m\u1ea5t m\u00e1t gi\u00fap t\u1ed1i \u01b0u h\u00f3a m\u00f4 h\u00ecnh v\u00e0 c\u1ea3i thi\u1ec7n hi\u1ec7u su\u1ea5t d\u1ef1 \u0111o\u00e1n.<\/p>\n<p><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-8.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-8-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-8-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298358 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-8.jpg\" alt=\"cong-thuc-dao-ham-8\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-8.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-8-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-8-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/p>\n<p><strong>\u1ee8ng d\u1ee5ng trong sinh h\u1ecdc<\/strong><\/p>\n<p>\u0110\u1ea1o h\u00e0m c\u0169ng c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 m\u00f4 ph\u1ecfng s\u1ef1 bi\u1ebfn \u0111\u1ed5i c\u1ee7a d\u1eef li\u1ec7u sinh h\u1ecdc. Ch\u1eb3ng h\u1ea1n nh\u01b0 t\u1ed1c \u0111\u1ed9 t\u0103ng tr\u01b0\u1edfng c\u1ee7a m\u1ed9t lo\u1ea1i vi khu\u1ea9n trong m\u1ed9t m\u00f4i tr\u01b0\u1eddng c\u1ee5 th\u1ec3.<\/p>\n<p><strong>T\u1ed1i \u01b0u h\u00f3a ti\u00eau th\u1ee5 n\u0103ng l\u01b0\u1ee3ng trong IoT<\/strong><\/p>\n<p>Trong Internet of Things (IoT), \u0111\u1ea1o h\u00e0m c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng \u0111\u1ec3 t\u1ed1i \u01b0u h\u00f3a ti\u00eau th\u1ee5 n\u0103ng l\u01b0\u1ee3ng c\u1ee7a thi\u1ebft b\u1ecb th\u00f4ng minh, gi\u00fap gia t\u0103ng hi\u1ec7u su\u1ea5t v\u00e0 tu\u1ed5i th\u1ecd pin.<\/p>\n<h2>C\u00e1ch ghi nh\u1edb c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m l\u00e2u<\/h2>\n<p>\u0110\u1ea7u ti\u00ean, h\u00e3y hi\u1ec3u c\u01a1 b\u1ea3n v\u1ec1 l\u00fd thuy\u1ebft \u0111\u1eb1ng sau c\u00e1c c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m. N\u1ebfu b\u1ea1n hi\u1ec3u \u00fd ngh\u0129a c\u1ee7a n\u00f3, vi\u1ec7c nh\u1edb n\u00f3 s\u1ebd d\u1ec5 d\u00e0ng h\u01a1n. L\u1eb7p l\u1ea1i c\u00f4ng th\u1ee9c nhi\u1ec1u l\u1ea7n c\u00f3 th\u1ec3 gi\u00fap n\u00e3o b\u1ed9 c\u1ee7a b\u1ea1n ghi nh\u1edb ch\u00fang. Vi\u1ec7c l\u00e0m n\u00e0y gi\u00fap t\u0103ng c\u01b0\u1eddng b\u1ed9 nh\u1edb d\u00e0i h\u1ea1n.<\/p>\n<p><strong><picture><source srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-9.jpg.webp 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-9-300x169.jpg.webp 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/webp-express\/webp-images\/uploads\/2023\/12\/cong-thuc-dao-ham-9-768x432.jpg.webp 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" type=\"image\/webp\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298360 webpexpress-processed\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-9.jpg\" alt=\"\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-9.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-9-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-9-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\"><\/picture><\/strong><\/p>\n<p>Nh\u00f3m c\u00e1c \u0111\u1ea1o h\u00e0m d\u1ef1a tr\u00ean t\u00ednh ch\u1ea5t chung c\u1ee7a ch\u00fang. V\u00ed d\u1ee5, nh\u00f3m c\u00e1c c\u00f4ng th\u1ee9c cho h\u00e0m s\u1ed1 m\u0169, logarit, l\u01b0\u1ee3ng gi\u00e1c, \u0111\u1ec3 nh\u1edb ch\u00fang d\u1ec5 d\u00e0ng h\u01a1n. \u00c1p d\u1ee5ng c\u00e1c c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m v\u00e0o b\u00e0i to\u00e1n th\u1ef1c t\u1ebf c\u00f3 th\u1ec3 gi\u00fap b\u1ea1n li\u00ean k\u1ebft ch\u00fang v\u1edbi \u1ee9ng d\u1ee5ng c\u1ee5 th\u1ec3 v\u00e0 d\u1ec5 nh\u1edb h\u01a1n.<\/p>\n<p>Gi\u1ea3i nhi\u1ec1u b\u00e0i t\u1eadp s\u1eed d\u1ee5ng c\u00e1c c\u00f4ng th\u1ee9c \u1ea5y. Th\u1ef1c h\u00e0nh l\u00e0 m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3 \u0111\u1ec3 ghi nh\u1edb v\u00e0 l\u00e0m quen v\u1edbi c\u00e1c c\u00f4ng th\u1ee9c trong nhi\u1ec1u ng\u1eef c\u1ea3nh kh\u00e1c nhau.<\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>\u0110\u1ea1o h\u00e0m kh\u00f4ng ch\u1ec9 l\u00e0 m\u1ed9t ph\u1ea7n quan tr\u1ecdng trong l\u0129nh v\u1ef1c to\u00e1n h\u1ecdc m\u00e0 c\u00f2n \u1ea3nh h\u01b0\u1edfng s\u00e2u r\u1ed9ng trong nhi\u1ec1u l\u0129nh v\u1ef1c \u1ee9ng d\u1ee5ng. Ch\u00fang ta \u0111\u00e3 t\u00ecm hi\u1ec3u v\u1ec1 c\u00e1c c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u01a1 b\u1ea3n. N\u00f3 bao g\u1ed3m \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 h\u1eb1ng, h\u00e0m s\u1ed1 m\u0169, h\u00e0m s\u1ed1 logarit, h\u00e0m s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c, v\u00e0 c\u00e1ch t\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 h\u1ee3p. Nh\u1eefng \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf c\u1ee7a \u0111\u1ea1o h\u00e0m m\u1edf ra nh\u1eefng kh\u1ea3 n\u0103ng m\u1edbi trong nhi\u1ec1u l\u0129nh v\u1ef1c. \u0110\u1ed3ng th\u1eddi ch\u1ee9ng minh s\u1ee9c m\u1ea1nh v\u00e0 t\u00ednh linh ho\u1ea1t c\u1ee7a n\u00f3 trong vi\u1ec7c gi\u1ea3i quy\u1ebft c\u00e1c v\u1ea5n \u0111\u1ec1 \u0111a d\u1ea1ng v\u00e0 ph\u1ee9c t\u1ea1p.<\/p>\n<p><strong>Xem th\u00eam:<\/strong><\/p>\n<ul>\n<li><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dien-tich-hinh-chu-nhat\/\">C\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh ch\u1eef nh\u1eadt ch\u00ednh x\u00e1c nh\u1ea5t<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-tinh-thoi-gian\/\">V\u1eadn t\u1ed1c l\u00e0 g\u00ec? C\u00f4ng th\u1ee9c t\u00ednh th\u1eddi gian, v\u1eadn t\u1ed1c, qu\u00e3ng \u0111\u01b0\u1eddng<\/a><\/strong><\/li>\n<li><strong><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/c\/\">C++ l\u00e0 g\u00ec? T\u1ed5ng h\u1ee3p ki\u1ebfn th\u1ee9c h\u1ecdc C++ c\u01a1 b\u1ea3n c\u1ef1c d\u1ec5 hi\u1ec3u<\/a><\/strong><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u0110\u1ea1o h\u00e0m sin l\u00e0 c\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n trong ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n l\u1edbp 11: (sin x)&#8217; = cos x. B\u00e0i vi\u1ebft h\u01b0\u1edbng d\u1eabn chi ti\u1ebft ch\u1ee9ng minh b\u1eb1ng \u0111\u1ecbnh ngh\u0129a \u0111\u1ea1o h\u00e0m, b\u1ea3ng \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7 c\u00e1c h\u00e0m l\u01b0\u1ee3ng gi\u00e1c (sin, cos, tan, cot\u2026), b\u00e0i t\u1eadp t\u00ednh \u0111\u1ea1o h\u00e0m sin u v\u00e0 \u1ee9ng d\u1ee5ng [&hellip;]<\/p>\n","protected":false},"author":100,"featured_media":298364,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3910,30453],"tags":[],"class_list":["post-297756","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-kham-pha","category-kien-thuc"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v24.2 (Yoast SEO v24.2) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0110\u1ea1o h\u00e0m sin: C\u00f4ng th\u1ee9c, ch\u1ee9ng minh, b\u1ea3ng l\u01b0\u1ee3ng gi\u00e1c v\u00e0 b\u00e0i t\u1eadp chi ti\u1ebft<\/title>\n<meta name=\"description\" content=\"\u0110\u1ea1o h\u00e0m sin = cos l\u00e0 c\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n l\u1edbp 11. H\u01b0\u1edbng d\u1eabn ch\u1ee9ng minh, b\u1ea3ng \u0111\u1ea1o h\u00e0m l\u01b0\u1ee3ng gi\u00e1c \u0111\u1ea7y \u0111\u1ee7, b\u00e0i t\u1eadp v\u00ed d\u1ee5 v\u00e0 \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf. Xem ngay \u0111\u1ec3 n\u1eafm v\u1eefng\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/\" \/>\n<meta property=\"og:locale\" content=\"vi_VN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0110\u1ea1o h\u00e0m sin: C\u00f4ng th\u1ee9c, ch\u1ee9ng minh v\u00e0 b\u00e0i t\u1eadp l\u01b0\u1ee3ng gi\u00e1c \u0111\u1ea7y \u0111\u1ee7\" \/>\n<meta property=\"og:description\" content=\"\u0110\u1ea1o h\u00e0m sin = cos l\u00e0 c\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n l\u1edbp 11. H\u01b0\u1edbng d\u1eabn ch\u1ee9ng minh, b\u1ea3ng \u0111\u1ea1o h\u00e0m l\u01b0\u1ee3ng gi\u00e1c \u0111\u1ea7y \u0111\u1ee7, b\u00e0i t\u1eadp v\u00ed d\u1ee5 v\u00e0 \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf. 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