{"id":123910,"date":"2025-04-03T15:57:58","date_gmt":"2025-04-03T08:57:58","guid":{"rendered":"https:\/\/phongvu.vn\/cong-nghe\/?p=123910"},"modified":"2025-04-04T12:03:01","modified_gmt":"2025-04-04T05:03:01","slug":"cong-thuc-dao-ham","status":"publish","type":"post","link":"https:\/\/phongvu.vn\/cong-nghe\/cong-thuc-dao-ham\/","title":{"rendered":"T\u1ed5ng h\u1ee3p c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u1ea7y \u0111\u1ee7 k\u00e8m b\u00e0i t\u1eadp d\u1ec5 hi\u1ec3u nh\u1ea5t"},"content":{"rendered":"\n<p>C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m l\u00e0 ki\u1ebfn th\u1ee9c quan tr\u1ecdng trong gi\u1ea3i t\u00edch, gi\u00fap gi\u1ea3i quy\u1ebft nhi\u1ec1u b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn t\u1ed1c \u0111\u1ed9 bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1. Trong b\u00e0i vi\u1ebft n\u00e0y, <a href=\"https:\/\/phongvu.vn\/cong-nghe\/\" target=\"_blank\" rel=\"noreferrer noopener\">Phong V\u0169 Tech News<\/a> s\u1ebd t\u1ed5ng h\u1ee3p \u0111\u1ea7y \u0111\u1ee7 c\u00e1c c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m quan tr\u1ecdng k\u00e8m theo b\u00e0i t\u1eadp minh h\u1ecda chi ti\u1ebft, gi\u00fap b\u1ea1n d\u1ec5 d\u00e0ng n\u1eafm v\u1eefng v\u00e0 \u00e1p d\u1ee5ng v\u00e0o th\u1ef1c t\u1ebf.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<ul>\n<li><a href=\"https:\/\/phongvu.vn\/cong-nghe\/dien-tich-hinh-thang\/\" target=\"_blank\" rel=\"noreferrer noopener\">\u201cB\u1ecf t\u00fai\u201d 4 c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh thang (vu\u00f4ng, c\u00e2n, th\u01b0\u1eddng) k\u00e8m b\u00e0i t\u1eadp chu\u1ea9n nh\u1ea5t 2025<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/phongvu.vn\/cong-nghe\/cach-tinh-dien-tich-hinh-vuong\/\" target=\"_blank\" data-type=\"URL\" data-id=\"https:\/\/phongvu.vn\/cong-nghe\/cach-tinh-dien-tich-hinh-vuong\/\" rel=\"noreferrer noopener\">M\u00e1ch b\u1ea1n c\u00f4ng th\u1ee9c t\u00ednh di\u1ec7n t\u00edch h\u00ecnh vu\u00f4ng c\u00f9ng b\u00e0i t\u1eadp (c\u00f3 \u0111\u00e1p \u00e1n)<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/phongvu.vn\/cong-nghe\/dien-tich-hinh-binh-hanh\/\" target=\"_blank\" rel=\"noreferrer noopener\">Di\u1ec7n t\u00edch h\u00ecnh b\u00ecnh h\u00e0nh: \u0110\u1ecbnh ngh\u0129a, c\u00f4ng th\u1ee9c v\u00e0 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i<\/a><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_55 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title \" >M\u1ee5c l\u1ee5c<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\" role=\"button\"><label for=\"item-6a264968a14e3\" ><span class=\"\"><span style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input aria-label=\"Toggle\" aria-label=\"item-6a264968a14e3\"  type=\"checkbox\" id=\"item-6a264968a14e3\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/phongvu.vn\/cong-nghe\/cong-thuc-dao-ham\/#Dao_ham_va_ung_dung_trong_toan_hoc\" title=\"\u0110\u1ea1o h\u00e0m v\u00e0 \u1ee9ng d\u1ee5ng trong to\u00e1n h\u1ecdc\">\u0110\u1ea1o h\u00e0m v\u00e0 \u1ee9ng d\u1ee5ng trong to\u00e1n h\u1ecdc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/phongvu.vn\/cong-nghe\/cong-thuc-dao-ham\/#Cong_thuc_dao_ham_co_ban\" title=\"C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u01a1 b\u1ea3n\">C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u01a1 b\u1ea3n<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/phongvu.vn\/cong-nghe\/cong-thuc-dao-ham\/#Dao_ham_cua_cac_ham_luong_giac_mu_va_logarit\" title=\"\u0110\u1ea1o h\u00e0m c\u1ee7a c\u00e1c h\u00e0m l\u01b0\u1ee3ng gi\u00e1c, m\u0169 v\u00e0 logarit\">\u0110\u1ea1o h\u00e0m c\u1ee7a c\u00e1c h\u00e0m l\u01b0\u1ee3ng gi\u00e1c, m\u0169 v\u00e0 logarit<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/phongvu.vn\/cong-nghe\/cong-thuc-dao-ham\/#Cong_thuc_dao_ham_nang_cao_tich_thuong_tong_hop\" title=\"C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m n\u00e2ng cao (t\u00edch, th\u01b0\u01a1ng, t\u1ed5ng h\u1ee3p)\">C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m n\u00e2ng cao (t\u00edch, th\u01b0\u01a1ng, t\u1ed5ng h\u1ee3p)<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/phongvu.vn\/cong-nghe\/cong-thuc-dao-ham\/#1_Quy_tac_dao_ham_cua_tich_hai_ham_so\" title=\"1. Quy t\u1eafc \u0111\u1ea1o h\u00e0m c\u1ee7a t\u00edch hai h\u00e0m s\u1ed1\">1. Quy t\u1eafc \u0111\u1ea1o h\u00e0m c\u1ee7a t\u00edch hai h\u00e0m s\u1ed1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/phongvu.vn\/cong-nghe\/cong-thuc-dao-ham\/#2_Quy_tac_dao_ham_cua_thuong_hai_ham_so\" title=\"2. Quy t\u1eafc \u0111\u1ea1o h\u00e0m c\u1ee7a th\u01b0\u01a1ng hai h\u00e0m s\u1ed1\">2. Quy t\u1eafc \u0111\u1ea1o h\u00e0m c\u1ee7a th\u01b0\u01a1ng hai h\u00e0m s\u1ed1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/phongvu.vn\/cong-nghe\/cong-thuc-dao-ham\/#3_Quy_tac_dao_ham_cua_ham_hop\" title=\"3. Quy t\u1eafc \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m h\u1ee3p\">3. Quy t\u1eafc \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m h\u1ee3p<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/phongvu.vn\/cong-nghe\/cong-thuc-dao-ham\/#Bai_tap_ap_dung_tu_de_den_kho_kem_loi_giai_chi_tiet\" title=\"B\u00e0i t\u1eadp \u00e1p d\u1ee5ng t\u1eeb d\u1ec5 \u0111\u1ebfn kh\u00f3 k\u00e8m l\u1eddi gi\u1ea3i chi ti\u1ebft\">B\u00e0i t\u1eadp \u00e1p d\u1ee5ng t\u1eeb d\u1ec5 \u0111\u1ebfn kh\u00f3 k\u00e8m l\u1eddi gi\u1ea3i chi ti\u1ebft<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/phongvu.vn\/cong-nghe\/cong-thuc-dao-ham\/#Bai_tap_co_ban_%E2%80%93_Tinh_dao_ham_cua_ham_so_don_gian\" title=\"B\u00e0i t\u1eadp c\u01a1 b\u1ea3n &#8211; T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 \u0111\u01a1n gi\u1ea3n\">B\u00e0i t\u1eadp c\u01a1 b\u1ea3n &#8211; T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 \u0111\u01a1n gi\u1ea3n<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/phongvu.vn\/cong-nghe\/cong-thuc-dao-ham\/#Bai_tap_trung_binh_%E2%80%93_Tinh_dao_ham_cua_ham_so_luong_giac\" title=\"B\u00e0i t\u1eadp trung b\u00ecnh &#8211; T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c\">B\u00e0i t\u1eadp trung b\u00ecnh &#8211; T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/phongvu.vn\/cong-nghe\/cong-thuc-dao-ham\/#Bai_tap_nang_cao_%E2%80%93_Tinh_dao_ham_cua_ham_so_phan_thuc\" title=\"B\u00e0i t\u1eadp n\u00e2ng cao &#8211; T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 ph\u00e2n th\u1ee9c\">B\u00e0i t\u1eadp n\u00e2ng cao &#8211; T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 ph\u00e2n th\u1ee9c<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/phongvu.vn\/cong-nghe\/cong-thuc-dao-ham\/#Ket_luan\" title=\"K\u1ebft lu\u1eadn\">K\u1ebft lu\u1eadn<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Dao_ham_va_ung_dung_trong_toan_hoc\"><\/span><strong>\u0110\u1ea1o h\u00e0m v\u00e0 \u1ee9ng d\u1ee5ng trong to\u00e1n h\u1ecdc<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0110\u1ea1o h\u00e0m l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m quan tr\u1ecdng trong gi\u1ea3i t\u00edch, bi\u1ec3u th\u1ecb t\u1ed1c \u0111\u1ed9 thay \u0111\u1ed5i c\u1ee7a h\u00e0m s\u1ed1 t\u1ea1i m\u1ed9t \u0111i\u1ec3m b\u1ea5t k\u1ef3. Nh\u1edd c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m, ta c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh s\u1ef1 bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1, t\u00ecm c\u1ef1c tr\u1ecb, ti\u1ebfp tuy\u1ebfn, v\u00e0 gi\u1ea3i quy\u1ebft nhi\u1ec1u b\u00e0i to\u00e1n th\u1ef1c t\u1ebf trong k\u1ef9 thu\u1eadt, v\u1eadt l\u00fd, kinh t\u1ebf.<\/p>\n\n\n\n<p>Trong to\u00e1n h\u1ecdc, \u0111\u00e0m h\u00e0m c\u1ee7a m\u1ed9t h\u00e0m s\u1ed1 t\u1ea1i m\u1ed9t \u0111i\u1ec3m l\u00e0 gi\u1edbi h\u1ea1n c\u1ee7a t\u1ec9 s\u1ed1 bi\u1ebfn thi\u00ean khi kho\u1ea3ng c\u00e1ch gi\u1eefa hai \u0111i\u1ec3m ti\u1ebfn d\u1ea7n \u0111\u1ebfn 0. C\u1ee5 th\u1ec3, n\u1ebfu h\u00e0m s\u1ed1 f(x) c\u00f3 \u0111\u1ea1o h\u00e0m t\u1ea1i \u0111i\u1ec3m x0\u200b, th\u00ec \u0111\u1ea1o h\u00e0m \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh theo c\u00f4ng th\u1ee9c:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-2-1024x640.jpg\" alt=\"\u0110\u1ea1o h\u00e0m c\u1ee7a m\u1ed9t h\u00e0m s\u1ed1 f(x) t\u1ea1i \u0111i\u1ec3m x=a \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 f&#039;(a) ho\u1eb7c \u0111\u01a1n gi\u1ea3n l\u00e0 f&#039;(x)\" class=\"wp-image-123911\" width=\"1022\" height=\"639\" srcset=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-2-1024x640.jpg 1024w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-2-300x188.jpg 300w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-2-768x480.jpg 768w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-2-150x94.jpg 150w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-2-600x375.jpg 600w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-2-696x435.jpg 696w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-2-1392x870.jpg 1392w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-2-1068x668.jpg 1068w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-2-672x420.jpg 672w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-2-1344x840.jpg 1344w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-2.jpg 1440w\" sizes=\"(max-width: 1022px) 100vw, 1022px\" title=\"\"><figcaption class=\"wp-element-caption\">\u0110\u1ea1o h\u00e0m c\u1ee7a m\u1ed9t h\u00e0m s\u1ed1 f(x) t\u1ea1i \u0111i\u1ec3m x=a \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 f'(a) ho\u1eb7c \u0111\u01a1n gi\u1ea3n l\u00e0 f'(x)<\/figcaption><\/figure>\n\n\n\n<p>N\u1ebfu gi\u1edbi h\u1ea1n n\u00e0y t\u1ed3n t\u1ea1i, ta n\u00f3i h\u00e0m s\u1ed1 f(x) c\u00f3 \u0111\u1ea1o h\u00e0m t\u1ea1i x0.<\/p>\n\n\n\n<p><strong>\u1ee8ng d\u1ee5ng c\u1ee7a \u0111\u1ea1o h\u00e0m trong to\u00e1n h\u1ecdc:<\/strong><\/p>\n\n\n\n<ul>\n<li><strong>X\u00e1c \u0111\u1ecbnh c\u1ef1c tr\u1ecb c\u1ee7a h\u00e0m s\u1ed1: <\/strong>Gi\u00fap t\u00ecm \u0111i\u1ec3m c\u1ef1c \u0111\u1ea1i, c\u1ef1c ti\u1ec3u \u0111\u1ec3 nghi\u00ean c\u1ee9u \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1.<\/li>\n\n\n\n<li><strong>T\u00ednh gi\u1edbi h\u1ea1n v\u00e0 li\u00ean t\u1ee5c:<\/strong> H\u1ed7 tr\u1ee3 trong vi\u1ec7c x\u00e1c \u0111\u1ecbnh t\u00ednh li\u00ean t\u1ee5c c\u1ee7a h\u00e0m s\u1ed1 t\u1ea1i m\u1ed9t \u0111i\u1ec3m.<\/li>\n\n\n\n<li><strong>X\u00e1c \u0111\u1ecbnh ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u1ed3 th\u1ecb h\u00e0m s\u1ed1: <\/strong>D\u00f9ng \u0111\u1ec3 t\u00ecm ph\u01b0\u01a1ng tr\u00ecnh ti\u1ebfp tuy\u1ebfn t\u1ea1i m\u1ed9t \u0111i\u1ec3m b\u1ea5t k\u1ef3.<\/li>\n\n\n\n<li><strong>Gi\u1ea3i quy\u1ebft b\u00e0i to\u00e1n t\u1ed1i \u01b0u h\u00f3a: <\/strong>\u1ee8ng d\u1ee5ng trong kinh t\u1ebf, k\u1ef9 thu\u1eadt \u0111\u1ec3 t\u00ecm gi\u00e1 tr\u1ecb t\u1ed1i \u01b0u c\u1ee7a m\u1ed9t \u0111\u1ea1i l\u01b0\u1ee3ng.<\/li>\n<\/ul>\n\n\n\n<p>Hi\u1ec3u r\u00f5 v\u00e0 v\u1eadn d\u1ee5ng th\u00e0nh th\u1ea1o c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m s\u1ebd gi\u00fap b\u1ea1n gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n to\u00e1n h\u1ecdc m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3 h\u01a1n.<\/p>\n\n\n\n<h2><span class=\"ez-toc-section\" id=\"Cong_thuc_dao_ham_co_ban\"><\/span><strong>C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u01a1 b\u1ea3n<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m l\u00e0 m\u1ed9t c\u00f4ng c\u1ee5 to\u00e1n h\u1ecdc quan tr\u1ecdng trong vi\u1ec7c t\u00ednh to\u00e1n \u0111\u1ed9 d\u1ed1c c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng cong t\u1ea1i m\u1ed9t \u0111i\u1ec3m c\u1ee5 th\u1ec3. \u0110\u1ea1o h\u00e0m c\u1ee7a m\u1ed9t h\u00e0m s\u1ed1 f(x) t\u1ea1i \u0111i\u1ec3m x = a \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 f\u2032(a) ho\u1eb7c \u0111\u01a1n gi\u1ea3n l\u00e0 f\u2032(x). \u0110\u1ea1o h\u00e0m gi\u00fap x\u00e1c \u0111\u1ecbnh xu h\u01b0\u1edbng bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1:<\/p>\n\n\n\n<ul>\n<li>N\u1ebfu f\u2032(x) &gt; 0, h\u00e0m s\u1ed1 t\u0103ng t\u1ea1i \u0111i\u1ec3m \u0111\u00f3.<\/li>\n\n\n\n<li>N\u1ebfu f\u2032(x) &lt; 0, h\u00e0m s\u1ed1 gi\u1ea3m t\u1ea1i \u0111i\u1ec3m \u0111\u00f3.<\/li>\n\n\n\n<li>N\u1ebfu f\u2032(x) = 0, h\u00e0m s\u1ed1 c\u00f3 th\u1ec3 \u0111\u1ea1t c\u1ef1c tr\u1ecb (c\u1ef1c \u0111\u1ea1i ho\u1eb7c c\u1ef1c ti\u1ec3u).<\/li>\n<\/ul>\n\n\n\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u01a1 b\u1ea3n c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 ph\u1ed5 bi\u1ebfn:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-3-1-1024x640.jpg\" alt=\"C\u00f4ng th\u1ee9c c\u1ee7a \u0111\u1ea1o h\u00e0m c\u01a1 b\u1ea3n\" class=\"wp-image-123913\" width=\"1024\" height=\"640\" srcset=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-3-1-1024x640.jpg 1024w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-3-1-300x188.jpg 300w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-3-1-768x480.jpg 768w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-3-1-150x94.jpg 150w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-3-1-600x375.jpg 600w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-3-1-696x435.jpg 696w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-3-1-1392x870.jpg 1392w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-3-1-1068x668.jpg 1068w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-3-1-672x420.jpg 672w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-3-1-1344x840.jpg 1344w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-3-1.jpg 1440w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" title=\"\"><figcaption class=\"wp-element-caption\">C\u00f4ng th\u1ee9c c\u1ee7a \u0111\u1ea1o h\u00e0m c\u01a1 b\u1ea3n<\/figcaption><\/figure>\n\n\n\n<p>Nh\u1eefng c\u00f4ng th\u1ee9c tr\u00ean l\u00e0 n\u1ec1n t\u1ea3ng quan tr\u1ecdng gi\u00fap b\u1ea1n gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn \u0111\u1ea1o h\u00e0m m\u1ed9t c\u00e1ch d\u1ec5 d\u00e0ng v\u00e0 ch\u00ednh x\u00e1c.<\/p>\n\n\n\n<p>Xem th\u00eam: <a href=\"https:\/\/phongvu.vn\/cong-nghe\/7-hang-dang-thuc-dang-nho\/\" target=\"_blank\" rel=\"noreferrer noopener\">7 h\u1eb1ng \u0111\u1eb3ng th\u1ee9c \u0111\u00e1ng nh\u1edb v\u00e0 c\u00e1ch v\u1eadn d\u1ee5ng trong b\u00e0i t\u1eadp to\u00e1n<\/a><\/p>\n\n\n\n<h2><span class=\"ez-toc-section\" id=\"Dao_ham_cua_cac_ham_luong_giac_mu_va_logarit\"><\/span><strong>\u0110\u1ea1o h\u00e0m c\u1ee7a c\u00e1c h\u00e0m l\u01b0\u1ee3ng gi\u00e1c, m\u0169 v\u00e0 logarit<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Trong gi\u1ea3i t\u00edch, \u0111\u1ea1o h\u00e0m c\u1ee7a c\u00e1c h\u00e0m l\u01b0\u1ee3ng gi\u00e1c, h\u00e0m s\u1ed1 m\u0169 v\u00e0 logarit \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c ph\u00e2n t\u00edch s\u1ef1 bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1, \u1ee9ng d\u1ee5ng r\u1ed9ng r\u00e3i trong v\u1eadt l\u00fd, k\u1ef9 thu\u1eadt v\u00e0 kinh t\u1ebf. Nh\u1eefng c\u00f4ng th\u1ee9c n\u00e0y gi\u00fap x\u00e1c \u0111\u1ecbnh t\u1ed1c \u0111\u1ed9 thay \u0111\u1ed5i c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 \u0111\u1eb7c bi\u1ec7t khi ch\u00fang xu\u1ea5t hi\u1ec7n trong c\u00e1c m\u00f4 h\u00ecnh to\u00e1n h\u1ecdc th\u1ef1c t\u1ebf.<\/p>\n\n\n\n<ul>\n<li><strong>\u0110\u1ed1i v\u1edbi h\u00e0m l\u01b0\u1ee3ng gi\u00e1c<\/strong>: \u0110\u1ea1o h\u00e0m gi\u00fap x\u00e1c \u0111\u1ecbnh s\u1ef1 thay \u0111\u1ed5i c\u1ee7a g\u00f3c v\u00e0 bi\u00ean \u0111\u1ed9, th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong dao \u0111\u1ed9ng, s\u00f3ng v\u00e0 k\u1ef9 thu\u1eadt s\u1ed1.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-4-1024x640.jpg\" alt=\"C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m l\u01b0\u1ee3ng gi\u00e1c\" class=\"wp-image-123914\" width=\"1024\" height=\"640\" srcset=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-4-1024x640.jpg 1024w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-4-300x188.jpg 300w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-4-768x480.jpg 768w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-4-150x94.jpg 150w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-4-600x375.jpg 600w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-4-696x435.jpg 696w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-4-1392x870.jpg 1392w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-4-1068x668.jpg 1068w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-4-672x420.jpg 672w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-4-1344x840.jpg 1344w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-4.jpg 1440w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" title=\"\"><figcaption class=\"wp-element-caption\">C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m l\u01b0\u1ee3ng gi\u00e1c<\/figcaption><\/figure>\n\n\n\n<ul>\n<li><strong>\u0110\u1ed1i v\u1edbi h\u00e0m m\u0169<\/strong>: \u0110\u1ea1o h\u00e0m th\u1ec3 hi\u1ec7n s\u1ef1 t\u0103ng tr\u01b0\u1edfng ho\u1eb7c suy gi\u1ea3m theo c\u1ea5p s\u1ed1 nh\u00e2n, \u1ee9ng d\u1ee5ng trong t\u00e0i ch\u00ednh, d\u00e2n s\u1ed1 h\u1ecdc v\u00e0 v\u1eadt l\u00fd h\u1ea1t nh\u00e2n. 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><\/li>\n\n\n\n<li><strong>\u0110\u1ed1i v\u1edbi h\u00e0m logarit<\/strong>: \u0110\u1ea1o h\u00e0m gi\u00fap x\u00e1c \u0111\u1ecbnh t\u1ed1c \u0111\u1ed9 thay \u0111\u1ed5i c\u1ee7a d\u1eef li\u1ec7u tr\u00ean thang \u0111o logarit, th\u01b0\u1eddng th\u1ea5y trong ph\u00e2n t\u00edch \u0111\u1ed9 l\u1edbn t\u00edn hi\u1ec7u v\u00e0 quy lu\u1eadt t\u0103ng tr\u01b0\u1edfng.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-5-1024x640.jpg\" alt=\"C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m logarit\" class=\"wp-image-123915\" width=\"1024\" height=\"640\" srcset=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-5-1024x640.jpg 1024w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-5-300x188.jpg 300w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-5-768x480.jpg 768w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-5-150x94.jpg 150w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-5-600x375.jpg 600w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-5-696x435.jpg 696w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-5-1392x870.jpg 1392w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-5-1068x668.jpg 1068w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-5-672x420.jpg 672w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-5-1344x840.jpg 1344w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-5.jpg 1440w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" title=\"\"><figcaption class=\"wp-element-caption\">C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m logarit<\/figcaption><\/figure>\n\n\n\n<h2><span class=\"ez-toc-section\" id=\"Cong_thuc_dao_ham_nang_cao_tich_thuong_tong_hop\"><\/span><strong>C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m n\u00e2ng cao (t\u00edch, th\u01b0\u01a1ng, t\u1ed5ng h\u1ee3p)<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>B\u00ean c\u1ea1nh c\u00e1c c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m c\u01a1 b\u1ea3n, trong nhi\u1ec1u b\u00e0i to\u00e1n th\u1ef1c t\u1ebf, ta c\u1ea7n t\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a c\u00e1c h\u00e0m s\u1ed1 ph\u1ee9c t\u1ea1p h\u01a1n nh\u01b0 t\u00edch c\u1ee7a hai h\u00e0m, th\u01b0\u01a1ng c\u1ee7a hai h\u00e0m ho\u1eb7c h\u00e0m h\u1ee3p. \u0110\u1ec3 l\u00e0m \u0111\u01b0\u1ee3c \u0111i\u1ec1u n\u00e0y, ch\u00fang ta s\u1eed d\u1ee5ng c\u00e1c quy t\u1eafc \u0111\u1ea1o h\u00e0m n\u00e2ng cao sau:<\/p>\n\n\n\n<h3><span class=\"ez-toc-section\" id=\"1_Quy_tac_dao_ham_cua_tich_hai_ham_so\"><\/span><strong>1. Quy t\u1eafc \u0111\u1ea1o h\u00e0m c\u1ee7a t\u00edch hai h\u00e0m s\u1ed1<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>N\u1ebfu u(x) v\u00e0 v(x) l\u00e0 hai h\u00e0m s\u1ed1 c\u00f3 \u0111\u1ea1o h\u00e0m, th\u00ec \u0111\u1ea1o h\u00e0m c\u1ee7a t\u00edch hai h\u00e0m \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c:&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-6-1024x640.jpg\" alt=\"\u0110\u1ea1o h\u00e0m c\u1ee7a t\u00edch hai h\u00e0m\" class=\"wp-image-123916\" width=\"1024\" height=\"640\" srcset=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-6-1024x640.jpg 1024w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-6-300x188.jpg 300w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-6-768x480.jpg 768w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-6-150x94.jpg 150w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-6-600x375.jpg 600w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-6-696x435.jpg 696w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-6-1392x870.jpg 1392w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-6-1068x668.jpg 1068w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-6-672x420.jpg 672w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-6-1344x840.jpg 1344w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-6.jpg 1440w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" title=\"\"><figcaption class=\"wp-element-caption\">\u0110\u1ea1o h\u00e0m c\u1ee7a t\u00edch hai h\u00e0m<\/figcaption><\/figure>\n\n\n\n<p>T\u1ee9c l\u00e0 \u0111\u1ea1o h\u00e0m c\u1ee7a t\u00edch hai h\u00e0m b\u1eb1ng \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m th\u1ee9 nh\u1ea5t nh\u00e2n v\u1edbi h\u00e0m th\u1ee9 hai, c\u1ed9ng v\u1edbi h\u00e0m th\u1ee9 nh\u1ea5t nh\u00e2n v\u1edbi \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m th\u1ee9 hai.<\/p>\n\n\n\n<h3><span class=\"ez-toc-section\" id=\"2_Quy_tac_dao_ham_cua_thuong_hai_ham_so\"><\/span><strong>2. Quy t\u1eafc \u0111\u1ea1o h\u00e0m c\u1ee7a th\u01b0\u01a1ng hai h\u00e0m s\u1ed1<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>N\u1ebfu u(x) v\u00e0 v(x) l\u00e0 hai h\u00e0m s\u1ed1 c\u00f3 \u0111\u1ea1o h\u00e0m v\u00e0 v(x) \u2260 0, th\u00ec \u0111\u1ea1o h\u00e0m c\u1ee7a th\u01b0\u01a1ng hai h\u00e0m \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-7-1024x640.jpg\" alt=\"\u0110\u1ea1o h\u00e0m c\u1ee7a th\u01b0\u01a1ng hai h\u00e0m\" class=\"wp-image-123917\" width=\"1024\" height=\"640\" srcset=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-7-1024x640.jpg 1024w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-7-300x188.jpg 300w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-7-768x480.jpg 768w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-7-150x94.jpg 150w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-7-600x375.jpg 600w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-7-696x435.jpg 696w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-7-1392x870.jpg 1392w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-7-1068x668.jpg 1068w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-7-672x420.jpg 672w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-7-1344x840.jpg 1344w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-7.jpg 1440w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" title=\"\"><figcaption class=\"wp-element-caption\">\u0110\u1ea1o h\u00e0m c\u1ee7a th\u01b0\u01a1ng hai h\u00e0m<\/figcaption><\/figure>\n\n\n\n<p>T\u1ee9c l\u00e0 \u0111\u1ea1o h\u00e0m c\u1ee7a th\u01b0\u01a1ng hai h\u00e0m b\u1eb1ng t\u1eed s\u1ed1 l\u00e0 \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 tr\u00ean nh\u00e2n v\u1edbi m\u1eabu s\u1ed1 tr\u1eeb \u0111i h\u00e0m s\u1ed1 tr\u00ean nh\u00e2n v\u1edbi \u0111\u1ea1o h\u00e0m c\u1ee7a m\u1eabu s\u1ed1, chia cho b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a m\u1eabu s\u1ed1.<\/p>\n\n\n\n<h3><span class=\"ez-toc-section\" id=\"3_Quy_tac_dao_ham_cua_ham_hop\"><\/span><strong>3. Quy t\u1eafc \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m h\u1ee3p<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<p>N\u1ebfu y = f(g(x)), trong \u0111\u00f3 g(x) l\u00e0 m\u1ed9t h\u00e0m s\u1ed1 v\u00e0 f(x) c\u0169ng l\u00e0 m\u1ed9t h\u00e0m s\u1ed1, th\u00ec \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m h\u1ee3p \u0111\u01b0\u1ee3c t\u00ednh theo c\u00f4ng th\u1ee9c:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-8-1024x640.jpg\" alt=\"\u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m h\u1ee3p\" class=\"wp-image-123918\" width=\"1024\" height=\"640\" srcset=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-8-1024x640.jpg 1024w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-8-300x188.jpg 300w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-8-768x480.jpg 768w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-8-150x94.jpg 150w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-8-600x375.jpg 600w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-8-696x435.jpg 696w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-8-1392x870.jpg 1392w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-8-1068x668.jpg 1068w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-8-672x420.jpg 672w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-8-1344x840.jpg 1344w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-8.jpg 1440w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" title=\"\"><figcaption class=\"wp-element-caption\">\u0110\u1ea1o h\u00e0m c\u1ee7a h\u00e0m h\u1ee3p<\/figcaption><\/figure>\n\n\n\n<p>T\u1ee9c l\u00e0 \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m h\u1ee3p b\u1eb1ng \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m b\u00ean ngo\u00e0i t\u1ea1i h\u00e0m b\u00ean trong nh\u00e2n v\u1edbi \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m b\u00ean trong.<\/p>\n\n\n\n<p>Nh\u1eefng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m n\u00e2ng cao n\u00e0y r\u1ea5t h\u1eefu \u00edch khi gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n ph\u1ee9c t\u1ea1p trong to\u00e1n h\u1ecdc v\u00e0 \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf.<\/p>\n\n\n\n<p>Xem th\u00eam: <a href=\"https:\/\/phongvu.vn\/cong-nghe\/cach-tinh-phan-tram-giam-gia\/\" target=\"_blank\" rel=\"noreferrer noopener\">G\u1ee3i \u00fd 3 c\u00e1ch t\u00ednh ph\u1ea7n tr\u0103m gi\u1ea3m gi\u00e1, t\u0103ng gi\u00e1 s\u1ea3n ph\u1ea9m<\/a><\/p>\n\n\n\n<h2><span class=\"ez-toc-section\" id=\"Bai_tap_ap_dung_tu_de_den_kho_kem_loi_giai_chi_tiet\"><\/span><strong>B\u00e0i t\u1eadp \u00e1p d\u1ee5ng t\u1eeb d\u1ec5 \u0111\u1ebfn kh\u00f3 k\u00e8m l\u1eddi gi\u1ea3i chi ti\u1ebft<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>\u0110\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 c\u00e1c c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m \u0111\u00e3 h\u1ecdc, ch\u00fang ta c\u00f9ng \u0111i qua m\u1ed9t s\u1ed1 b\u00e0i t\u1eadp \u00e1p d\u1ee5ng t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao, k\u00e8m l\u1eddi gi\u1ea3i chi ti\u1ebft. Vi\u1ec7c th\u1ef1c h\u00e0nh v\u1edbi c\u00e1c b\u00e0i to\u00e1n c\u1ee5 th\u1ec3 s\u1ebd gi\u00fap b\u1ea1n kh\u00f4ng ch\u1ec9 ghi nh\u1edb c\u00f4ng th\u1ee9c t\u1ed1t h\u01a1n m\u00e0 c\u00f2n hi\u1ec3u c\u00e1ch v\u1eadn d\u1ee5ng ch\u00fang v\u00e0o c\u00e1c t\u00ecnh hu\u1ed1ng th\u1ef1c t\u1ebf. M\u1ed7i b\u00e0i t\u1eadp \u0111\u1ec1u cung c\u1ea5p m\u1ed9t c\u00e1ch ti\u1ebfp c\u1eadn tr\u1ef1c quan, gi\u00fap b\u1ea1n n\u1eafm v\u1eefng ki\u1ebfn th\u1ee9c m\u1ed9t c\u00e1ch d\u1ec5 d\u00e0ng:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-9-1024x640.jpg\" alt=\"B\u00e0i t\u1eadp \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m\" class=\"wp-image-123920\" width=\"1024\" height=\"640\" srcset=\"https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-9-1024x640.jpg 1024w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-9-300x188.jpg 300w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-9-768x480.jpg 768w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-9-150x94.jpg 150w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-9-600x375.jpg 600w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-9-696x435.jpg 696w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-9-1392x870.jpg 1392w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-9-1068x668.jpg 1068w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-9-672x420.jpg 672w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-9-1344x840.jpg 1344w, https:\/\/phongvu.vn\/cong-nghe\/wp-content\/uploads\/2025\/04\/cong-thuc-dao-ham-9.jpg 1440w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" title=\"\"><figcaption class=\"wp-element-caption\">B\u00e0i t\u1eadp \u00e1p d\u1ee5ng c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m<\/figcaption><\/figure>\n\n\n\n<h3><span class=\"ez-toc-section\" id=\"Bai_tap_co_ban_%E2%80%93_Tinh_dao_ham_cua_ham_so_don_gian\"><\/span><strong>B\u00e0i t\u1eadp c\u01a1 b\u1ea3n &#8211; T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 \u0111\u01a1n gi\u1ea3n<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<ol>\n<li><strong>T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 y = x\u00b3 + 2x\u00b2 &#8211; 5x + 1.<\/strong><\/li>\n<\/ol>\n\n\n\n<ul>\n<li>L\u1eddi gi\u1ea3i: y&#8217; = 3x\u00b2 + 4x &#8211; 5.<\/li>\n<\/ul>\n\n\n\n<ol start=\"2\">\n<li><strong>T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 y = sin x + cos x.<\/strong><\/li>\n<\/ol>\n\n\n\n<ul>\n<li>L\u1eddi gi\u1ea3i: y&#8217; = cos x &#8211; sin x.<\/li>\n<\/ul>\n\n\n\n<ol start=\"3\">\n<li><strong>T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 y = e^x + ln x.<\/strong><\/li>\n<\/ol>\n\n\n\n<ul>\n<li>L\u1eddi gi\u1ea3i : y&#8217; = e^x + 1\/x.<\/li>\n<\/ul>\n\n\n\n<h3><span class=\"ez-toc-section\" id=\"Bai_tap_trung_binh_%E2%80%93_Tinh_dao_ham_cua_ham_so_luong_giac\"><\/span><strong>B\u00e0i t\u1eadp trung b\u00ecnh &#8211; T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 l\u01b0\u1ee3ng gi\u00e1c<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<ol>\n<li><strong>T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 y = x.sin x.<\/strong><\/li>\n<\/ol>\n\n\n\n<ul>\n<li>L\u1eddi gi\u1ea3i: y&#8217; = sin x + x.cos x.<\/li>\n<\/ul>\n\n\n\n<ol start=\"2\">\n<li><strong>T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 y = (x\u00b2 + 1)\/(x &#8211; 1).<\/strong><\/li>\n<\/ol>\n\n\n\n<ul>\n<li>L\u1eddi gi\u1ea3i: y&#8217; = (2x(x-1) &#8211; (x\u00b2+1))\/(x-1)\u00b2 = (x\u00b2-2x-1)\/(x-1)\u00b2.<\/li>\n<\/ul>\n\n\n\n<ol start=\"3\">\n<li><strong>T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 y = sin(2x + 1).<\/strong><\/li>\n<\/ol>\n\n\n\n<ul>\n<li>L\u1eddi gi\u1ea3i: y&#8217; = 2cos(2x + 1).<\/li>\n<\/ul>\n\n\n\n<h3><span class=\"ez-toc-section\" id=\"Bai_tap_nang_cao_%E2%80%93_Tinh_dao_ham_cua_ham_so_phan_thuc\"><\/span><strong>B\u00e0i t\u1eadp n\u00e2ng cao &#8211; T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 ph\u00e2n th\u1ee9c<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n\n<ol>\n<li><strong>T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 y = \u221a(x\u00b2 + 1).<\/strong><\/li>\n<\/ol>\n\n\n\n<ul>\n<li>L\u1eddi gi\u1ea3i: y&#8217; = x\/\u221a(x\u00b2 + 1).<\/li>\n<\/ul>\n\n\n\n<ol start=\"2\">\n<li><strong>T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 y = ln(sin x).<\/strong><\/li>\n<\/ol>\n\n\n\n<ul>\n<li>L\u1eddi gi\u1ea3i: y&#8217; = cos x\/sin x = cot x.<\/li>\n<\/ul>\n\n\n\n<ol start=\"3\">\n<li><strong>T\u00ednh \u0111\u1ea1o h\u00e0m c\u1ee7a h\u00e0m s\u1ed1 y = e^(sin x).<\/strong><\/li>\n<\/ol>\n\n\n\n<ul>\n<li>L\u1eddi gi\u1ea3i: y&#8217; = cos(x) * e^(sin(x)).<\/li>\n<\/ul>\n\n\n\n<p>C\u00e1c b\u00e0i t\u1eadp tr\u00ean gi\u00fap c\u1ee7ng c\u1ed1 ki\u1ebfn th\u1ee9c v\u1ec1 \u0111\u1ea1o h\u00e0m t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao. Vi\u1ec7c luy\u1ec7n t\u1eadp th\u01b0\u1eddng xuy\u00ean s\u1ebd gi\u00fap b\u1ea1n th\u00e0nh th\u1ea1o c\u00e1c ph\u01b0\u01a1ng ph\u00e1p t\u00ednh to\u00e1n v\u00e0 \u00e1p d\u1ee5ng v\u00e0o th\u1ef1c t\u1ebf m\u1ed9t c\u00e1ch hi\u1ec7u qu\u1ea3.<\/p>\n\n\n\n<div class=\"pv-products-card\"><div class=\"pv-products-title\"><div>Tham kh\u1ea3o m\u1ed9t s\u1ed1 d\u00f2ng laptop n\u1ed5i b\u1eadt, b\u00e1n ch\u1ea1y t\u1ea1i Phong V\u0169 d\u01b0\u1edbi \u0111\u00e2y:<\/div><\/div><div class=\"pv-products\" data-type=\"carousel\" data-key=\"product-area\" data-skus=\"220101409,230703418,230703419,230704076,231002798,231004204,240302749,240302752,240502377,240602773\"><\/div><\/div>\n\n\n\n<h2><span class=\"ez-toc-section\" id=\"Ket_luan\"><\/span><strong>K\u1ebft lu\u1eadn<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m l\u00e0 ki\u1ebfn th\u1ee9c quan tr\u1ecdng gi\u00fap b\u1ea1n gi\u1ea3i quy\u1ebft nhi\u1ec1u b\u00e0i to\u00e1n trong to\u00e1n h\u1ecdc v\u00e0 \u1ee9ng d\u1ee5ng th\u1ef1c t\u1ebf. Qua b\u00e0i vi\u1ebft n\u00e0y, Phong V\u0169 Tech News \u0111\u00e3 t\u1ed5ng h\u1ee3p \u0111\u1ea7y \u0111\u1ee7 c\u00e1c c\u00f4ng th\u1ee9c t\u1eeb c\u01a1 b\u1ea3n \u0111\u1ebfn n\u00e2ng cao, k\u00e8m theo b\u00e0i t\u1eadp minh h\u1ecda chi ti\u1ebft. Hy v\u1ecdng r\u1eb1ng nh\u1eefng ki\u1ebfn th\u1ee9c n\u00e0y s\u1ebd gi\u00fap b\u1ea1n n\u1eafm v\u1eefng v\u00e0 \u00e1p d\u1ee5ng \u0111\u1ea1o h\u00e0m m\u1ed9t c\u00e1ch d\u1ec5 d\u00e0ng. \u0110\u1eebng qu\u00ean luy\u1ec7n t\u1eadp th\u01b0\u1eddng xuy\u00ean \u0111\u1ec3 n\u00e2ng cao k\u1ef9 n\u0103ng t\u00ednh to\u00e1n v\u00e0 hi\u1ec3u s\u00e2u h\u01a1n v\u1ec1 ch\u1ee7 \u0111\u1ec1 n\u00e0y!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>C\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m l\u00e0 ki\u1ebfn th\u1ee9c quan tr\u1ecdng trong gi\u1ea3i t\u00edch, gi\u00fap gi\u1ea3i quy\u1ebft nhi\u1ec1u b\u00e0i to\u00e1n li\u00ean quan \u0111\u1ebfn t\u1ed1c \u0111\u1ed9 bi\u1ebfn thi\u00ean c\u1ee7a h\u00e0m s\u1ed1. Trong b\u00e0i vi\u1ebft n\u00e0y, Phong V\u0169 Tech News s\u1ebd t\u1ed5ng h\u1ee3p \u0111\u1ea7y \u0111\u1ee7 c\u00e1c c\u00f4ng th\u1ee9c \u0111\u1ea1o h\u00e0m quan tr\u1ecdng k\u00e8m theo b\u00e0i t\u1eadp minh h\u1ecda chi [&hellip;]<\/p>\n","protected":false},"author":34,"featured_media":123919,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[74],"tags":[],"_links":{"self":[{"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/posts\/123910"}],"collection":[{"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/users\/34"}],"replies":[{"embeddable":true,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/comments?post=123910"}],"version-history":[{"count":2,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/posts\/123910\/revisions"}],"predecessor-version":[{"id":124046,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/posts\/123910\/revisions\/124046"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/media\/123919"}],"wp:attachment":[{"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/media?parent=123910"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/categories?post=123910"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/phongvu.vn\/cong-nghe\/wp-json\/wp\/v2\/tags?post=123910"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}