{"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":"2026-11-05T14:10:20","modified_gmt":"2026-11-05T07:10:20","slug":"cong-thuc-dao-ham","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/","title":{"rendered":"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7: l\u01b0\u1ee3ng gi\u00e1c, m\u0169, logarit, h\u00e0m h\u1ee3p v\u00e0 v\u00ed d\u1ee5"},"content":{"rendered":"<p><strong>B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u01a1 b\u1ea3n g\u1ed3m: (C)&#8217; = 0, (x\u207f)&#8217; = n\u00b7x\u207f\u207b\u00b9, (sin x)&#8217; = cos x, (cos x)&#8217; = \u2212sin x, (tan x)&#8217; = 1\/cos\u00b2x, (e\u02e3)&#8217; = e\u02e3, (ln x)&#8217; = 1\/x, c\u00f9ng c\u00e1c quy t\u1eafc t\u1ed5ng, t\u00edch, th\u01b0\u01a1ng v\u00e0 \u0111\u1ea1o h\u00e0m h\u00e0m h\u1ee3p (u)&#8217; theo x.<\/strong> B\u00e0i vi\u1ebft t\u1ed5ng h\u1ee3p \u0111\u1ea7y \u0111\u1ee7 b\u1ea3ng \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 s\u01a1 c\u1ea5p, \u0111\u1ea1o h\u00e0m l\u01b0\u1ee3ng gi\u00e1c, m\u0169 \u2013 logarit, \u0111\u1ea1o h\u00e0m c\u1ea5p cao, k\u00e8m v\u00ed d\u1ee5 t\u00ednh t\u1eebng b\u01b0\u1edbc theo ch\u01b0\u01a1ng tr\u00ecnh To\u00e1n l\u1edbp 11.<\/p>\n<p><strong>T\u00f3m t\u1eaft nhanh:<\/strong><\/p>\n<ul>\n<li><strong>Quy t\u1eafc:<\/strong> (u \u00b1 v)&#8217; = u&#8217; \u00b1 v&#8217;; (uv)&#8217; = u&#8217;v + uv&#8217;; (u\/v)&#8217; = (u&#8217;v \u2212 uv&#8217;)\/v\u00b2.<\/li>\n<li><strong>H\u00e0m h\u1ee3p:<\/strong> y = f(u(x)) th\u00ec y&#8217; = f'(u)\u00b7u&#8217;.<\/li>\n<li><strong>L\u01b0\u1ee3ng gi\u00e1c:<\/strong> (sin u)&#8217; = u&#8217;\u00b7cos u; (cos u)&#8217; = \u2212u&#8217;\u00b7sin u; (tan u)&#8217; = u&#8217;\/cos\u00b2u; (cot u)&#8217; = \u2212u&#8217;\/sin\u00b2u.<\/li>\n<li><strong>M\u0169 \u2013 logarit:<\/strong> (e\u1d58)&#8217; = u&#8217;\u00b7e\u1d58; (a\u1d58)&#8217; = u&#8217;\u00b7a\u1d58\u00b7ln a; (ln u)&#8217; = u&#8217;\/u; (log\u2090u)&#8217; = u&#8217;\/(u\u00b7ln a).<\/li>\n<\/ul>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter size-full wp-image-298356\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-1.jpg\" alt=\"\u0110\u1ecbnh ngh\u0129a \u0111\u1ea1o h\u00e0m v\u00e0 c\u00e1c quy t\u1eafc t\u00ednh \u0111\u1ea1o h\u00e0m c\u01a1 b\u1ea3n\" 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\" \/><\/p>\n<h2>\u0110\u1ea1o h\u00e0m l\u00e0 g\u00ec?<\/h2>\n<p>\u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 y = f(x) t\u1ea1i \u0111i\u1ec3m x\u2080 l\u00e0 gi\u1edbi h\u1ea1n (n\u1ebfu c\u00f3) c\u1ee7a t\u1ec9 s\u1ed1 gi\u1eefa s\u1ed1 gia c\u1ee7a h\u00e0m s\u1ed1 v\u00e0 s\u1ed1 gia c\u1ee7a bi\u1ebfn s\u1ed1 khi s\u1ed1 gia bi\u1ebfn s\u1ed1 d\u1ea7n v\u1ec1 0:<\/p>\n<p style=\"text-align: center;\"><strong>f'(x\u2080) = lim<sub>\u0394x\u21920<\/sub> \u0394y\/\u0394x = lim<sub>x\u2192x\u2080<\/sub> [f(x) \u2212 f(x\u2080)] \/ (x \u2212 x\u2080)<\/strong><\/p>\n<p>\u00dd ngh\u0129a: \u0111\u1ea1o h\u00e0m cho bi\u1ebft t\u1ed1c \u0111\u1ed9 thay \u0111\u1ed5i t\u1ee9c th\u1eddi c\u1ee7a h\u00e0m s\u1ed1. V\u1ec1 h\u00ecnh h\u1ecdc, f'(x\u2080) l\u00e0 h\u1ec7 s\u1ed1 g\u00f3c c\u1ee7a ti\u1ebfp tuy\u1ebfn v\u1edbi \u0111\u1ed3 th\u1ecb t\u1ea1i \u0111i\u1ec3m c\u00f3 ho\u00e0nh \u0111\u1ed9 x\u2080; v\u1ec1 v\u1eadt l\u00fd, \u0111\u1ea1o h\u00e0m c\u1ee7a qu\u00e3ng \u0111\u01b0\u1eddng theo th\u1eddi gian l\u00e0 v\u1eadn t\u1ed1c t\u1ee9c th\u1eddi.<\/p>\n<h2>Quy t\u1eafc t\u00ednh \u0111\u1ea1o h\u00e0m<\/h2>\n<table>\n<thead>\n<tr>\n<th>Quy t\u1eafc<\/th>\n<th>C\u00f4ng th\u1ee9c<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>T\u1ed5ng, hi\u1ec7u<\/td>\n<td>(u \u00b1 v)&#8217; = u&#8217; \u00b1 v&#8217;<\/td>\n<\/tr>\n<tr>\n<td>T\u00edch<\/td>\n<td>(u\u00b7v)&#8217; = u&#8217;\u00b7v + u\u00b7v&#8217;<\/td>\n<\/tr>\n<tr>\n<td>H\u1eb1ng s\u1ed1 nh\u00e2n<\/td>\n<td>(k\u00b7u)&#8217; = k\u00b7u&#8217;<\/td>\n<\/tr>\n<tr>\n<td>Th\u01b0\u01a1ng<\/td>\n<td>(u\/v)&#8217; = (u&#8217;\u00b7v \u2212 u\u00b7v&#8217;) \/ v\u00b2 (v \u2260 0)<\/td>\n<\/tr>\n<tr>\n<td>Ngh\u1ecbch \u0111\u1ea3o<\/td>\n<td>(k\/u)&#8217; = \u2212k\u00b7u&#8217; \/ u\u00b2<\/td>\n<\/tr>\n<tr>\n<td>H\u00e0m h\u1ee3p<\/td>\n<td>y&#8217;\u2093 = y&#8217;\u1d64 \u00b7 u&#8217;\u2093<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>B\u1ea3ng \u0111\u1ea1o h\u00e0m c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 s\u01a1 c\u1ea5p c\u01a1 b\u1ea3n<\/h2>\n<table>\n<thead>\n<tr>\n<th>H\u00e0m s\u1ed1 y = f(x)<\/th>\n<th>\u0110\u1ea1o h\u00e0m<\/th>\n<th>H\u00e0m h\u1ee3p y = f(u)<\/th>\n<th>\u0110\u1ea1o h\u00e0m<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>C (h\u1eb1ng s\u1ed1)<\/td>\n<td>0<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>x<\/td>\n<td>1<\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>x<sup>\u03b1<\/sup><\/td>\n<td>\u03b1\u00b7x<sup>\u03b1\u22121<\/sup><\/td>\n<td>u<sup>\u03b1<\/sup><\/td>\n<td>\u03b1\u00b7u<sup>\u03b1\u22121<\/sup>\u00b7u&#8217;<\/td>\n<\/tr>\n<tr>\n<td>\u221ax<\/td>\n<td>1 \/ (2\u221ax)<\/td>\n<td>\u221au<\/td>\n<td>u&#8217; \/ (2\u221au)<\/td>\n<\/tr>\n<tr>\n<td>1\/x<\/td>\n<td>\u22121 \/ x\u00b2<\/td>\n<td>1\/u<\/td>\n<td>\u2212u&#8217; \/ u\u00b2<\/td>\n<\/tr>\n<tr>\n<td>sin x<\/td>\n<td>cos x<\/td>\n<td>sin u<\/td>\n<td>u&#8217;\u00b7cos u<\/td>\n<\/tr>\n<tr>\n<td>cos x<\/td>\n<td>\u2212sin x<\/td>\n<td>cos u<\/td>\n<td>\u2212u&#8217;\u00b7sin u<\/td>\n<\/tr>\n<tr>\n<td>tan x<\/td>\n<td>1\/cos\u00b2x = 1 + tan\u00b2x<\/td>\n<td>tan u<\/td>\n<td>u&#8217; \/ cos\u00b2u<\/td>\n<\/tr>\n<tr>\n<td>cot x<\/td>\n<td>\u22121\/sin\u00b2x = \u2212(1 + cot\u00b2x)<\/td>\n<td>cot u<\/td>\n<td>\u2212u&#8217; \/ sin\u00b2u<\/td>\n<\/tr>\n<tr>\n<td>e\u02e3<\/td>\n<td>e\u02e3<\/td>\n<td>e\u1d58<\/td>\n<td>u&#8217;\u00b7e\u1d58<\/td>\n<\/tr>\n<tr>\n<td>a\u02e3<\/td>\n<td>a\u02e3\u00b7ln a<\/td>\n<td>a\u1d58<\/td>\n<td>u&#8217;\u00b7a\u1d58\u00b7ln a<\/td>\n<\/tr>\n<tr>\n<td>ln x<\/td>\n<td>1\/x<\/td>\n<td>ln u<\/td>\n<td>u&#8217;\/u<\/td>\n<\/tr>\n<tr>\n<td>log\u2090x<\/td>\n<td>1 \/ (x\u00b7ln a)<\/td>\n<td>log\u2090u<\/td>\n<td>u&#8217; \/ (u\u00b7ln a)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-298355\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-2.jpg\" alt=\"B\u1ea3ng \u0111\u1ea1o h\u00e0m c\u00e1c h\u00e0m s\u1ed1 s\u01a1 c\u1ea5p v\u00e0 h\u00e0m h\u1ee3p\" 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\" \/><\/p>\n<p>C\u00f4ng th\u1ee9c t\u00ednh nhanh cho h\u00e0m ph\u00e2n th\u1ee9c: (ax + b)\/(cx + d) c\u00f3 \u0111\u1ea1o h\u00e0m (ad \u2212 bc)\/(cx + d)\u00b2; (ax\u00b2 + bx + c)\/(ex + f) c\u00f3 \u0111\u1ea1o h\u00e0m (aex\u00b2 + 2afx + bf \u2212 ce)\/(ex + f)\u00b2. Hai b\u00e0i ri\u00eang v\u1ec1 <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dao-ham-cua-1-x\/\">\u0111\u1ea1o h\u00e0m c\u1ee7a 1\/x<\/a> v\u00e0 <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dao-ham-e-mu-u-la-gi\/\">\u0111\u1ea1o h\u00e0m e m\u0169 u<\/a> c\u00f3 v\u00ed d\u1ee5 chi ti\u1ebft h\u01a1n.<\/p>\n<h2>\u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c<\/h2>\n<p>\u0110\u1ea1o h\u00e0m c\u1ee7a sin x \u0111\u01b0\u1ee3c ch\u1ee9ng minh t\u1eeb \u0111\u1ecbnh ngh\u0129a: sin(x + h) \u2212 sin x = 2cos(x + h\/2)\u00b7sin(h\/2), chia cho h v\u00e0 cho h \u2192 0, d\u00f9ng gi\u1edbi h\u1ea1n sin t \/ t \u2192 1, ta \u0111\u01b0\u1ee3c (sin x)&#8217; = cos x. C\u00e1c h\u00e0m c\u00f2n l\u1ea1i suy ra b\u1eb1ng quy t\u1eafc th\u01b0\u01a1ng, v\u00ed d\u1ee5 tan x = sin x \/ cos x n\u00ean (tan x)&#8217; = (cos\u00b2x + sin\u00b2x)\/cos\u00b2x = 1\/cos\u00b2x.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-298353\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-4.jpg\" alt=\"\u0110\u1ea1o h\u00e0m c\u1ee7a c\u00e1c h\u00e0m l\u01b0\u1ee3ng gi\u00e1c v\u00e0 l\u01b0\u1ee3ng gi\u00e1c ng\u01b0\u1ee3c\" 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\" \/><\/p>\n<p>B\u1ea3ng tr\u00ean c\u00f3 th\u00eam \u0111\u1ea1o h\u00e0m c\u1ee7a c\u00e1c h\u00e0m l\u01b0\u1ee3ng gi\u00e1c ng\u01b0\u1ee3c: (arcsin x)&#8217; = 1\/\u221a(1 \u2212 x\u00b2), (arccos x)&#8217; = \u22121\/\u221a(1 \u2212 x\u00b2), (arctan x)&#8217; = 1\/(1 + x\u00b2). C\u00e1c c\u00f4ng th\u1ee9c bi\u1ebfn \u0111\u1ed5i l\u01b0\u1ee3ng gi\u00e1c c\u1ea7n d\u00f9ng khi r\u00fat g\u1ecdn \u0111\u1ea1o h\u00e0m c\u00f3 trong b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-luong-giac\/\">b\u1ea3ng c\u00f4ng th\u1ee9c l\u01b0\u1ee3ng gi\u00e1c<\/a>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298359\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-10.jpg\" alt=\"\u0110\u1ed3 th\u1ecb y = sin x\" 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\" \/><\/p>\n<h2>C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u1ea5p cao<\/h2>\n<p>\u0110\u1ea1o h\u00e0m c\u1ea5p n l\u00e0 \u0111\u1ea1o h\u00e0m c\u1ee7a \u0111\u1ea1o h\u00e0m c\u1ea5p n \u2212 1, k\u00fd hi\u1ec7u y\u207d\u207f\u207e. M\u1ed9t s\u1ed1 c\u00f4ng th\u1ee9c th\u01b0\u1eddng d\u00f9ng:<\/p>\n<ul>\n<li>(x\u1d50)\u207d\u207f\u207e = m(m \u2212 1)\u2026(m \u2212 n + 1)\u00b7x\u1d50\u207b\u207f n\u1ebfu m \u2265 n; b\u1eb1ng 0 n\u1ebfu m nguy\u00ean d\u01b0\u01a1ng v\u00e0 m < n.<\/li>\n<li>(e\u1d4f\u02e3)\u207d\u207f\u207e = k\u207f\u00b7e\u1d4f\u02e3; (a\u02e3)\u207d\u207f\u207e = (ln a)\u207f\u00b7a\u02e3.<\/li>\n<li>(sin ax)\u207d\u207f\u207e = a\u207f\u00b7sin(ax + n\u03c0\/2); (cos ax)\u207d\u207f\u207e = a\u207f\u00b7cos(ax + n\u03c0\/2).<\/li>\n<li>(ln x)\u207d\u207f\u207e = (\u22121)\u207f\u207b\u00b9\u00b7(n \u2212 1)! \/ x\u207f.<\/li>\n<li>[1\/(ax + b)]\u207d\u207f\u207e = (\u22121)\u207f\u00b7a\u207f\u00b7n! \/ (ax + b)\u207f\u207a\u00b9. V\u00ed d\u1ee5 [1\/(2x + 1)]&#8221;&#8217; = \u221248\/(2x + 1)\u2074.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298354\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-3.jpg\" alt=\"C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u1ea5p cao\" 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\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298363\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-12.jpg\" alt=\"K\u00fd hi\u1ec7u \u0111\u1ea1o h\u00e0m c\u1ea5p n\" 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\" \/><\/p>\n<h2>V\u00ed d\u1ee5 t\u00ednh \u0111\u1ea1o h\u00e0m c\u00f3 l\u1eddi gi\u1ea3i<\/h2>\n<p><strong>V\u00ed d\u1ee5 1 (\u0111a th\u1ee9c):<\/strong> y = x\u00b3 \u2212 3x\u00b2 + 2 \u21d2 y&#8217; = 3x\u00b2 \u2212 6x.<\/p>\n<p><strong>V\u00ed d\u1ee5 2 (ph\u00e2n th\u1ee9c):<\/strong> y = (2x + 1)\/(x \u2212 1) \u21d2 y&#8217; = (2\u00b7(\u22121) \u2212 1\u00b71)\/(x \u2212 1)\u00b2 = \u22123\/(x \u2212 1)\u00b2.<\/p>\n<p><strong>V\u00ed d\u1ee5 3 (t\u00edch):<\/strong> y = x\u00b7sin x \u21d2 y&#8217; = sin x + x\u00b7cos x.<\/p>\n<p><strong>V\u00ed d\u1ee5 4 (h\u00e0m h\u1ee3p l\u01b0\u1ee3ng gi\u00e1c):<\/strong> y = sin 2x \u21d2 y&#8217; = 2cos 2x; y = tan 3x \u21d2 y&#8217; = 3\/cos\u00b23x; y = cos\u00b3x \u21d2 y&#8217; = \u22123cos\u00b2x\u00b7sin x.<\/p>\n<p><strong>V\u00ed d\u1ee5 5 (c\u0103n, m\u0169, logarit):<\/strong> y = \u221a(3x + 1) \u21d2 y&#8217; = 3\/(2\u221a(3x + 1)); y = e<sup>x\u00b2<\/sup> \u21d2 y&#8217; = 2x\u00b7e<sup>x\u00b2<\/sup>; y = ln(x\u00b2 + 1) \u21d2 y&#8217; = 2x\/(x\u00b2 + 1); y = 2\u02e3 \u21d2 y&#8217; = 2\u02e3\u00b7ln 2.<\/p>\n<p><strong>V\u00ed d\u1ee5 6 (v\u1eadn t\u1ed1c):<\/strong> M\u1ed9t v\u1eadt chuy\u1ec3n \u0111\u1ed9ng theo ph\u01b0\u01a1ng tr\u00ecnh s(t) = 5t\u00b2 \u2212 3t + 2 (m\u00e9t, gi\u00e2y). V\u1eadn t\u1ed1c v(t) = s'(t) = 10t \u2212 3, t\u1ea1i t = 2 gi\u00e2y l\u00e0 v = 17 m\/s; gia t\u1ed1c a(t) = v'(t) = 10 m\/s\u00b2.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298357\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-7.jpg\" alt=\"\u0110\u1ea1o h\u00e0m c\u1ee7a qu\u00e3ng \u0111\u01b0\u1eddng theo th\u1eddi gian l\u00e0 v\u1eadn t\u1ed1c\" 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\" \/><\/p>\n<p>Mu\u1ed1n ki\u1ec3m tra nhanh k\u1ebft qu\u1ea3, c\u00f3 th\u1ec3 d\u00f9ng m\u00e1y t\u00ednh c\u1ea7m tay theo b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/cach-bam-may-tinh-lim\/\">c\u00e1ch b\u1ea5m m\u00e1y t\u00ednh \u0111\u1ea1o h\u00e0m, lim<\/a>.<\/p>\n<h2>\u1ee8ng d\u1ee5ng c\u1ee7a \u0111\u1ea1o h\u00e0m<\/h2>\n<ul>\n<li><strong>X\u00e9t t\u00ednh \u0111\u01a1n \u0111i\u1ec7u:<\/strong> y&#8217; > 0 tr\u00ean m\u1ed9t kho\u1ea3ng th\u00ec h\u00e0m \u0111\u1ed3ng bi\u1ebfn, y&#8217; < 0 th\u00ec ngh\u1ecbch bi\u1ebfn, xem b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/tinh-don-dieu-cua-ham-so\/\">t\u00ednh \u0111\u01a1n \u0111i\u1ec7u c\u1ee7a h\u00e0m s\u1ed1<\/a>.<\/li>\n<li><strong>T\u00ecm c\u1ef1c tr\u1ecb, gi\u00e1 tr\u1ecb l\u1edbn nh\u1ea5t \u2013 nh\u1ecf nh\u1ea5t:<\/strong> gi\u1ea3i y&#8217; = 0 v\u00e0 x\u00e9t d\u1ea5u y&#8217;.<\/li>\n<li><strong>Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn:<\/strong> y = f'(x\u2080)(x \u2212 x\u2080) + f(x\u2080).<\/li>\n<li><strong>V\u1eadt l\u00fd:<\/strong> v\u1eadn t\u1ed1c l\u00e0 \u0111\u1ea1o h\u00e0m c\u1ee7a qu\u00e3ng \u0111\u01b0\u1eddng, gia t\u1ed1c l\u00e0 \u0111\u1ea1o h\u00e0m c\u1ee7a v\u1eadn t\u1ed1c.<\/li>\n<li><strong>Kinh t\u1ebf, k\u1ef9 thu\u1eadt:<\/strong> t\u00ecm m\u1ee9c s\u1ea3n l\u01b0\u1ee3ng l\u00e0m chi ph\u00ed nh\u1ecf nh\u1ea5t ho\u1eb7c l\u1ee3i nhu\u1eadn l\u1edbn nh\u1ea5t.<\/li>\n<\/ul>\n<h2>M\u1eb9o ghi nh\u1edb b\u1ea3ng \u0111\u1ea1o h\u00e0m<\/h2>\n<ul>\n<li>H\u1ecdc theo c\u1eb7p: m\u1ed7i c\u00f4ng th\u1ee9c c\u1ee7a x \u0111i k\u00e8m c\u00f4ng th\u1ee9c c\u1ee7a u, ch\u1ec9 c\u1ea7n nh\u00e2n th\u00eam u&#8217;.<\/li>\n<li>Nh\u1edb d\u1ea5u tr\u1eeb \u1edf nh\u00f3m &#8220;co&#8221;: cos, cot \u0111\u1ec1u c\u00f3 \u0111\u1ea1o h\u00e0m mang d\u1ea5u \u00e2m.<\/li>\n<li>T\u1ef1 ch\u1ee9ng minh l\u1ea1i tan, cot t\u1eeb quy t\u1eafc th\u01b0\u01a1ng thay v\u00ec h\u1ecdc thu\u1ed9c m\u00e1y m\u00f3c.<\/li>\n<li>L\u00e0m \u00edt nh\u1ea5t 10 b\u00e0i h\u00e0m h\u1ee3p m\u1ed7i ng\u00e0y trong tu\u1ea7n \u0111\u1ea7u.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-298360\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-9.jpg\" alt=\"M\u1eb9o ghi nh\u1edb c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m\" 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\" \/><\/p>\n<p>B\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/dao-ham-lop-11\/\">\u0111\u1ea1o h\u00e0m l\u1edbp 11<\/a> c\u00f3 th\u00eam h\u1ec7 th\u1ed1ng b\u00e0i t\u1eadp theo t\u1eebng d\u1ea1ng.<\/p>\n<h2>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p<\/h2>\n<h3>B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u01a1 b\u1ea3n g\u1ed3m nh\u1eefng g\u00ec?<\/h3>\n<p>G\u1ed3m \u0111\u1ea1o h\u00e0m c\u1ee7a h\u1eb1ng s\u1ed1, x\u207f, \u221ax, 1\/x, sin x, cos x, tan x, cot x, e\u02e3, a\u02e3, ln x, log\u2090x v\u00e0 c\u00e1c d\u1ea1ng h\u00e0m h\u1ee3p t\u01b0\u01a1ng \u1ee9ng c\u1ee7a u, c\u00f9ng quy t\u1eafc t\u1ed5ng, t\u00edch, th\u01b0\u01a1ng.<\/p>\n<h3>\u0110\u1ea1o h\u00e0m c\u1ee7a sin x l\u00e0 g\u00ec?<\/h3>\n<p>(sin x)&#8217; = cos x; v\u1edbi h\u00e0m h\u1ee3p, (sin u)&#8217; = u&#8217;\u00b7cos u, v\u00ed d\u1ee5 (sin 2x)&#8217; = 2cos 2x.<\/p>\n<h3>\u0110\u1ea1o h\u00e0m c\u1ee7a tan x l\u00e0 g\u00ec?<\/h3>\n<p>(tan x)&#8217; = 1\/cos\u00b2x = 1 + tan\u00b2x, v\u1edbi cos x \u2260 0.<\/p>\n<h3>C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u1ee7a m\u1ed9t th\u01b0\u01a1ng l\u00e0 g\u00ec?<\/h3>\n<p>(u\/v)&#8217; = (u&#8217;\u00b7v \u2212 u\u00b7v&#8217;)\/v\u00b2, v\u1edbi v \u2260 0.<\/p>\n<h3>\u0110\u1ea1o h\u00e0m h\u00e0m h\u1ee3p t\u00ednh th\u1ebf n\u00e0o?<\/h3>\n<p>N\u1ebfu y = f(u) v\u1edbi u = u(x) th\u00ec y&#8217; = f'(u)\u00b7u&#8217;. V\u00ed d\u1ee5 y = (x\u00b2 + 1)\u00b3 th\u00ec y&#8217; = 3(x\u00b2 + 1)\u00b2\u00b72x.<\/p>\n<h3>\u0110\u1ea1o h\u00e0m h\u1ecdc \u1edf l\u1edbp m\u1ea5y?<\/h3>\n<p>\u0110\u1ea1o h\u00e0m \u0111\u01b0\u1ee3c h\u1ecdc \u1edf To\u00e1n l\u1edbp 11 v\u00e0 d\u00f9ng \u0111\u1ec3 kh\u1ea3o s\u00e1t h\u00e0m s\u1ed1 \u1edf To\u00e1n l\u1edbp 12.<\/p>\n<p><script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@type\": \"FAQPage\",\n  \"mainEntity\": [\n    {\n      \"@type\": \"Question\",\n      \"name\": \"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u01a1 b\u1ea3n g\u1ed3m nh\u1eefng g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"G\u1ed3m \u0111\u1ea1o h\u00e0m c\u1ee7a h\u1eb1ng s\u1ed1, x\u207f, \u221ax, 1\/x, sin x, cos x, tan x, cot x, e\u02e3, a\u02e3, ln x, log\u2090x v\u00e0 c\u00e1c d\u1ea1ng h\u00e0m h\u1ee3p t\u01b0\u01a1ng \u1ee9ng c\u1ee7a u, c\u00f9ng quy t\u1eafc t\u1ed5ng, t\u00edch, th\u01b0\u01a1ng.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"\u0110\u1ea1o h\u00e0m c\u1ee7a sin x l\u00e0 g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"(sin x)' = cos x; v\u1edbi h\u00e0m h\u1ee3p, (sin u)' = u'\u00b7cos u, v\u00ed d\u1ee5 (sin 2x)' = 2cos 2x.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"\u0110\u1ea1o h\u00e0m c\u1ee7a tan x l\u00e0 g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"(tan x)' = 1\/cos\u00b2x = 1 + tan\u00b2x, v\u1edbi cos x \u2260 0.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u1ee7a m\u1ed9t th\u01b0\u01a1ng l\u00e0 g\u00ec?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"(u\/v)' = (u'\u00b7v \u2212 u\u00b7v')\/v\u00b2, v\u1edbi v \u2260 0.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"\u0110\u1ea1o h\u00e0m h\u00e0m h\u1ee3p t\u00ednh th\u1ebf n\u00e0o?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"N\u1ebfu y = f(u) v\u1edbi u = u(x) th\u00ec y' = f'(u)\u00b7u'. V\u00ed d\u1ee5 y = (x\u00b2 + 1)\u00b3 th\u00ec y' = 3(x\u00b2 + 1)\u00b2\u00b72x.\"\n      }\n    },\n    {\n      \"@type\": \"Question\",\n      \"name\": \"\u0110\u1ea1o h\u00e0m h\u1ecdc \u1edf l\u1edbp m\u1ea5y?\",\n      \"acceptedAnswer\": {\n        \"@type\": \"Answer\",\n        \"text\": \"\u0110\u1ea1o h\u00e0m \u0111\u01b0\u1ee3c h\u1ecdc \u1edf To\u00e1n l\u1edbp 11 v\u00e0 d\u00f9ng \u0111\u1ec3 kh\u1ea3o s\u00e1t h\u00e0m s\u1ed1 \u1edf To\u00e1n l\u1edbp 12.\"\n      }\n    }\n  ]\n}\n<\/script><\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m ch\u1ec9 g\u1ed3m kho\u1ea3ng 13 c\u00f4ng th\u1ee9c c\u01a1 b\u1ea3n v\u00e0 6 quy t\u1eafc; n\u1eafm ch\u1eafc c\u1eb7p c\u00f4ng th\u1ee9c x \u2013 u v\u00e0 quy t\u1eafc h\u00e0m h\u1ee3p l\u00e0 t\u00ednh \u0111\u01b0\u1ee3c \u0111\u1ea1o h\u00e0m c\u1ee7a h\u1ea7u h\u1ebft h\u00e0m s\u1ed1 trong ch\u01b0\u01a1ng tr\u00ecnh ph\u1ed5 th\u00f4ng. H\u00e3y luy\u1ec7n c\u00e1c v\u00ed d\u1ee5 \u1edf tr\u00ean, r\u1ed3i chuy\u1ec3n sang \u1ee9ng d\u1ee5ng x\u00e9t t\u00ednh \u0111\u01a1n \u0111i\u1ec7u v\u00e0 c\u1ef1c tr\u1ecb \u0111\u1ec3 th\u1ea5y r\u00f5 vai tr\u00f2 c\u1ee7a \u0111\u1ea1o h\u00e0m.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u01a1 b\u1ea3n g\u1ed3m: (C)&#8217; = 0, (x\u207f)&#8217; = n\u00b7x\u207f\u207b\u00b9, (sin x)&#8217; = cos x, (cos x)&#8217; = \u2212sin x, (tan x)&#8217; = 1\/cos\u00b2x, (e\u02e3)&#8217; = e\u02e3, (ln x)&#8217; = 1\/x, c\u00f9ng c\u00e1c quy t\u1eafc t\u1ed5ng, t\u00edch, th\u01b0\u01a1ng v\u00e0 \u0111\u1ea1o h\u00e0m h\u00e0m h\u1ee3p (u)&#8217; theo x. B\u00e0i vi\u1ebft t\u1ed5ng h\u1ee3p \u0111\u1ea7y [&hellip;]<\/p>\n","protected":false},"author":100,"featured_media":298364,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m","_yoast_wpseo_title":"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7 v\u00e0 v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i","_yoast_wpseo_metadesc":"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7: quy t\u1eafc t\u1ed5ng, t\u00edch, th\u01b0\u01a1ng, h\u00e0m h\u1ee3p, \u0111\u1ea1o h\u00e0m l\u01b0\u1ee3ng gi\u00e1c, m\u0169, logarit, \u0111\u1ea1o h\u00e0m c\u1ea5p cao k\u00e8m v\u00ed d\u1ee5 t\u00ednh \u0111\u1ea1o h\u00e0m t\u1eebng b\u01b0\u1edbc.","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 v27.3 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7 v\u00e0 v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i<\/title>\n<meta name=\"description\" content=\"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7: quy t\u1eafc t\u1ed5ng, t\u00edch, th\u01b0\u01a1ng, h\u00e0m h\u1ee3p, \u0111\u1ea1o h\u00e0m l\u01b0\u1ee3ng gi\u00e1c, m\u0169, logarit, \u0111\u1ea1o h\u00e0m c\u1ea5p cao k\u00e8m v\u00ed d\u1ee5 t\u00ednh \u0111\u1ea1o h\u00e0m t\u1eebng b\u01b0\u1edbc.\" \/>\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=\"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7: l\u01b0\u1ee3ng gi\u00e1c, m\u0169, logarit, h\u00e0m h\u1ee3p v\u00e0 v\u00ed d\u1ee5\" \/>\n<meta property=\"og:description\" content=\"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7: quy t\u1eafc t\u1ed5ng, t\u00edch, th\u01b0\u01a1ng, h\u00e0m h\u1ee3p, \u0111\u1ea1o h\u00e0m l\u01b0\u1ee3ng gi\u00e1c, m\u0169, logarit, \u0111\u1ea1o h\u00e0m c\u1ea5p cao k\u00e8m v\u00ed d\u1ee5 t\u00ednh \u0111\u1ea1o h\u00e0m t\u1eebng b\u01b0\u1edbc.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/\" \/>\n<meta property=\"og:site_name\" content=\"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/hoanghamobilecom\" \/>\n<meta property=\"article:published_time\" content=\"2023-12-25T09:27:34+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-11-05T07:10:20+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-14.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"628\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"L\u00ea Ng\u00e2n\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u0110\u01b0\u1ee3c vi\u1ebft b\u1edfi\" \/>\n\t<meta name=\"twitter:data1\" content=\"L\u00ea Ng\u00e2n\" \/>\n\t<meta name=\"twitter:label2\" content=\"\u01af\u1edbc t\u00ednh th\u1eddi gian \u0111\u1ecdc\" \/>\n\t<meta name=\"twitter:data2\" content=\"14 ph\u00fat\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/cong-thuc-dao-ham\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/cong-thuc-dao-ham\\\/\"},\"author\":{\"name\":\"L\u00ea Ng\u00e2n\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#\\\/schema\\\/person\\\/884ed48b993a843d1344bd7e441507a0\"},\"headline\":\"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7: l\u01b0\u1ee3ng gi\u00e1c, m\u0169, logarit, h\u00e0m h\u1ee3p v\u00e0 v\u00ed d\u1ee5\",\"datePublished\":\"2023-12-25T09:27:34+00:00\",\"dateModified\":\"2026-11-05T07:10:20+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/cong-thuc-dao-ham\\\/\"},\"wordCount\":1683,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/cong-thuc-dao-ham\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/wp-content\\\/uploads\\\/2023\\\/12\\\/cong-thuc-dao-ham-14.jpg\",\"articleSection\":[\"Kh\u00e1m Ph\u00e1\",\"Ki\u1ebfn Th\u1ee9c\"],\"inLanguage\":\"vi\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/cong-thuc-dao-ham\\\/#respond\"]}],\"copyrightYear\":\"2023\",\"copyrightHolder\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#organization\"}},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/cong-thuc-dao-ham\\\/\",\"url\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/cong-thuc-dao-ham\\\/\",\"name\":\"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7 v\u00e0 v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/cong-thuc-dao-ham\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/cong-thuc-dao-ham\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/wp-content\\\/uploads\\\/2023\\\/12\\\/cong-thuc-dao-ham-14.jpg\",\"datePublished\":\"2023-12-25T09:27:34+00:00\",\"dateModified\":\"2026-11-05T07:10:20+00:00\",\"description\":\"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7: quy t\u1eafc t\u1ed5ng, t\u00edch, th\u01b0\u01a1ng, h\u00e0m h\u1ee3p, \u0111\u1ea1o h\u00e0m l\u01b0\u1ee3ng gi\u00e1c, m\u0169, logarit, \u0111\u1ea1o h\u00e0m c\u1ea5p cao k\u00e8m v\u00ed d\u1ee5 t\u00ednh \u0111\u1ea1o h\u00e0m t\u1eebng b\u01b0\u1edbc.\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/cong-thuc-dao-ham\\\/#breadcrumb\"},\"inLanguage\":\"vi\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/cong-thuc-dao-ham\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"vi\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/cong-thuc-dao-ham\\\/#primaryimage\",\"url\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/wp-content\\\/uploads\\\/2023\\\/12\\\/cong-thuc-dao-ham-14.jpg\",\"contentUrl\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/wp-content\\\/uploads\\\/2023\\\/12\\\/cong-thuc-dao-ham-14.jpg\",\"width\":1200,\"height\":628,\"caption\":\"cong-thuc-dao-ham-14\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/cong-thuc-dao-ham\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Trang ch\u1ee7\",\"item\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7: l\u01b0\u1ee3ng gi\u00e1c, m\u0169, logarit, h\u00e0m h\u1ee3p v\u00e0 v\u00ed d\u1ee5\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#website\",\"url\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/\",\"name\":\"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"vi\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#organization\",\"name\":\"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile\",\"url\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"vi\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/wp-content\\\/uploads\\\/2021\\\/12\\\/logo-text.png\",\"contentUrl\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/wp-content\\\/uploads\\\/2021\\\/12\\\/logo-text.png\",\"width\":256,\"height\":37,\"caption\":\"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile\"},\"image\":{\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/hoanghamobilecom\"]},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/#\\\/schema\\\/person\\\/884ed48b993a843d1344bd7e441507a0\",\"name\":\"L\u00ea Ng\u00e2n\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"vi\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/567e42772371f5d833ad4ba9c2a32e35557dd95857e4649d487eae1a618952bb?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/567e42772371f5d833ad4ba9c2a32e35557dd95857e4649d487eae1a618952bb?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/567e42772371f5d833ad4ba9c2a32e35557dd95857e4649d487eae1a618952bb?s=96&d=mm&r=g\",\"caption\":\"L\u00ea Ng\u00e2n\"},\"description\":\"L\u00ea Ng\u00e2n l\u00e0 t\u00e1c gi\u1ea3 n\u1ed9i dung tr\u00ean chuy\u00ean trang Tin t\u1ee9c c\u00f4ng ngh\u1ec7 c\u1ee7a Ho\u00e0ng H\u00e0 Mobile. C\u00e1c b\u00e0i vi\u1ebft t\u1eadp trung v\u00e0o robot h\u00fat b\u1ee5i, m\u00e1y l\u1ecdc kh\u00f4ng kh\u00ed, \u0111i\u1ec1u h\u00f2a v\u00e0 thi\u1ebft b\u1ecb gia d\u1ee5ng, cung c\u1ea5p th\u00f4ng tin l\u1ef1a ch\u1ecdn v\u00e0 h\u01b0\u1edbng d\u1eabn s\u1eed d\u1ee5ng theo t\u1eebng nhu c\u1ea7u.\",\"url\":\"https:\\\/\\\/hoanghamobile.com\\\/tin-tuc\\\/author\\\/le-ngan\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7 v\u00e0 v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i","description":"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7: quy t\u1eafc t\u1ed5ng, t\u00edch, th\u01b0\u01a1ng, h\u00e0m h\u1ee3p, \u0111\u1ea1o h\u00e0m l\u01b0\u1ee3ng gi\u00e1c, m\u0169, logarit, \u0111\u1ea1o h\u00e0m c\u1ea5p cao k\u00e8m v\u00ed d\u1ee5 t\u00ednh \u0111\u1ea1o h\u00e0m t\u1eebng b\u01b0\u1edbc.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/","og_locale":"vi_VN","og_type":"article","og_title":"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7: l\u01b0\u1ee3ng gi\u00e1c, m\u0169, logarit, h\u00e0m h\u1ee3p v\u00e0 v\u00ed d\u1ee5","og_description":"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7: quy t\u1eafc t\u1ed5ng, t\u00edch, th\u01b0\u01a1ng, h\u00e0m h\u1ee3p, \u0111\u1ea1o h\u00e0m l\u01b0\u1ee3ng gi\u00e1c, m\u0169, logarit, \u0111\u1ea1o h\u00e0m c\u1ea5p cao k\u00e8m v\u00ed d\u1ee5 t\u00ednh \u0111\u1ea1o h\u00e0m t\u1eebng b\u01b0\u1edbc.","og_url":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/","og_site_name":"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile","article_publisher":"https:\/\/www.facebook.com\/hoanghamobilecom","article_published_time":"2023-12-25T09:27:34+00:00","article_modified_time":"2026-11-05T07:10:20+00:00","og_image":[{"width":1200,"height":628,"url":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-14.jpg","type":"image\/jpeg"}],"author":"L\u00ea Ng\u00e2n","twitter_card":"summary_large_image","twitter_misc":{"\u0110\u01b0\u1ee3c vi\u1ebft b\u1edfi":"L\u00ea Ng\u00e2n","\u01af\u1edbc t\u00ednh th\u1eddi gian \u0111\u1ecdc":"14 ph\u00fat"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/#article","isPartOf":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/"},"author":{"name":"L\u00ea Ng\u00e2n","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#\/schema\/person\/884ed48b993a843d1344bd7e441507a0"},"headline":"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7: l\u01b0\u1ee3ng gi\u00e1c, m\u0169, logarit, h\u00e0m h\u1ee3p v\u00e0 v\u00ed d\u1ee5","datePublished":"2023-12-25T09:27:34+00:00","dateModified":"2026-11-05T07:10:20+00:00","mainEntityOfPage":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/"},"wordCount":1683,"commentCount":0,"publisher":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#organization"},"image":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/#primaryimage"},"thumbnailUrl":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-14.jpg","articleSection":["Kh\u00e1m Ph\u00e1","Ki\u1ebfn Th\u1ee9c"],"inLanguage":"vi","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/#respond"]}],"copyrightYear":"2023","copyrightHolder":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#organization"}},{"@type":"WebPage","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/","url":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/","name":"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7 v\u00e0 v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i","isPartOf":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#website"},"primaryImageOfPage":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/#primaryimage"},"image":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/#primaryimage"},"thumbnailUrl":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-14.jpg","datePublished":"2023-12-25T09:27:34+00:00","dateModified":"2026-11-05T07:10:20+00:00","description":"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7: quy t\u1eafc t\u1ed5ng, t\u00edch, th\u01b0\u01a1ng, h\u00e0m h\u1ee3p, \u0111\u1ea1o h\u00e0m l\u01b0\u1ee3ng gi\u00e1c, m\u0169, logarit, \u0111\u1ea1o h\u00e0m c\u1ea5p cao k\u00e8m v\u00ed d\u1ee5 t\u00ednh \u0111\u1ea1o h\u00e0m t\u1eebng b\u01b0\u1edbc.","breadcrumb":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/#breadcrumb"},"inLanguage":"vi","potentialAction":[{"@type":"ReadAction","target":["https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/"]}]},{"@type":"ImageObject","inLanguage":"vi","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/#primaryimage","url":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-14.jpg","contentUrl":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2023\/12\/cong-thuc-dao-ham-14.jpg","width":1200,"height":628,"caption":"cong-thuc-dao-ham-14"},{"@type":"BreadcrumbList","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/cong-thuc-dao-ham\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Trang ch\u1ee7","item":"https:\/\/hoanghamobile.com\/tin-tuc\/"},{"@type":"ListItem","position":2,"name":"B\u1ea3ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7: l\u01b0\u1ee3ng gi\u00e1c, m\u0169, logarit, h\u00e0m h\u1ee3p v\u00e0 v\u00ed d\u1ee5"}]},{"@type":"WebSite","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#website","url":"https:\/\/hoanghamobile.com\/tin-tuc\/","name":"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile","description":"","publisher":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/hoanghamobile.com\/tin-tuc\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"vi"},{"@type":"Organization","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#organization","name":"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile","url":"https:\/\/hoanghamobile.com\/tin-tuc\/","logo":{"@type":"ImageObject","inLanguage":"vi","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#\/schema\/logo\/image\/","url":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2021\/12\/logo-text.png","contentUrl":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2021\/12\/logo-text.png","width":256,"height":37,"caption":"Tin t\u1ee9c c\u00f4ng ngh\u1ec7 - HoangHaMobile"},"image":{"@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/hoanghamobilecom"]},{"@type":"Person","@id":"https:\/\/hoanghamobile.com\/tin-tuc\/#\/schema\/person\/884ed48b993a843d1344bd7e441507a0","name":"L\u00ea Ng\u00e2n","image":{"@type":"ImageObject","inLanguage":"vi","@id":"https:\/\/secure.gravatar.com\/avatar\/567e42772371f5d833ad4ba9c2a32e35557dd95857e4649d487eae1a618952bb?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/567e42772371f5d833ad4ba9c2a32e35557dd95857e4649d487eae1a618952bb?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/567e42772371f5d833ad4ba9c2a32e35557dd95857e4649d487eae1a618952bb?s=96&d=mm&r=g","caption":"L\u00ea Ng\u00e2n"},"description":"L\u00ea Ng\u00e2n l\u00e0 t\u00e1c gi\u1ea3 n\u1ed9i dung tr\u00ean chuy\u00ean trang Tin t\u1ee9c c\u00f4ng ngh\u1ec7 c\u1ee7a Ho\u00e0ng H\u00e0 Mobile. C\u00e1c b\u00e0i vi\u1ebft t\u1eadp trung v\u00e0o robot h\u00fat b\u1ee5i, m\u00e1y l\u1ecdc kh\u00f4ng kh\u00ed, \u0111i\u1ec1u h\u00f2a v\u00e0 thi\u1ebft b\u1ecb gia d\u1ee5ng, cung c\u1ea5p th\u00f4ng tin l\u1ef1a ch\u1ecdn v\u00e0 h\u01b0\u1edbng d\u1eabn s\u1eed d\u1ee5ng theo t\u1eebng nhu c\u1ea7u.","url":"https:\/\/hoanghamobile.com\/tin-tuc\/author\/le-ngan\/"}]}},"_links":{"self":[{"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/posts\/297756","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/users\/100"}],"replies":[{"embeddable":true,"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/comments?post=297756"}],"version-history":[{"count":3,"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/posts\/297756\/revisions"}],"predecessor-version":[{"id":620803,"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/posts\/297756\/revisions\/620803"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/media\/298364"}],"wp:attachment":[{"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/media?parent=297756"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/categories?post=297756"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hoanghamobile.com\/tin-tuc\/wp-json\/wp\/v2\/tags?post=297756"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}