{"id":332,"date":"2023-07-06T06:56:27","date_gmt":"2023-07-06T06:56:27","guid":{"rendered":"https:\/\/mathority.org\/ar\/%d9%85%d8%b5%d9%81%d9%88%d9%81%d8%a9-%d9%8a%d8%b9%d9%82%d9%88%d8%a8%d9%8a%d8%a9-%d9%8a%d8%b9%d9%82%d9%88%d8%a8%d9%8a%d8%a7%d9%86\/"},"modified":"2023-07-06T06:56:27","modified_gmt":"2023-07-06T06:56:27","slug":"%d9%85%d8%b5%d9%81%d9%88%d9%81%d8%a9-%d9%8a%d8%b9%d9%82%d9%88%d8%a8%d9%8a%d8%a9-%d9%8a%d8%b9%d9%82%d9%88%d8%a8%d9%8a%d8%a7%d9%86","status":"publish","type":"post","link":"https:\/\/mathority.org\/ar\/%d9%85%d8%b5%d9%81%d9%88%d9%81%d8%a9-%d9%8a%d8%b9%d9%82%d9%88%d8%a8%d9%8a%d8%a9-%d9%8a%d8%b9%d9%82%d9%88%d8%a8%d9%8a%d8%a7%d9%86\/","title":{"rendered":"\u0645\u0635\u0641\u0648\u0641\u0629 \u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0648\u064a\u0639\u0642\u0648\u0628\u064a\u0629"},"content":{"rendered":"<p style=\";text-align:right;direction:rtl\">\u0633\u062a\u062c\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0645\u0627 \u0647\u064a \u0645\u0635\u0641\u0648\u0641\u0629 \u062c\u0627\u0643\u0648\u0628\u064a \u0648\u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628\u0647\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u062b\u0627\u0644. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0644\u062f\u064a\u0643 \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u0639\u0644\u0649 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u062d\u062a\u0649 \u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u064a\u0647\u0627. \u0633\u062a\u0631\u0649 \u0623\u064a\u0636\u064b\u0627 \u0633\u0628\u0628 \u0623\u0647\u0645\u064a\u0629 \u0645\u062d\u062f\u062f \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629\u060c \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629. \u0648\u0623\u062e\u064a\u0631\u0627\u060c \u0646\u0648\u0636\u062d \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0642\u064a\u0645\u0647\u0627 \u0647\u0630\u0647 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0645\u0639 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0623\u062e\u0631\u0649 \u0648\u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0627\u0644\u062a\u064a \u0644\u0647\u0627.<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0645\u0627 \u0647\u064a \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629\u061f<\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0647\u0648 \u0643\u0645\u0627 \u064a\u0644\u064a:<\/p>\n<p class=\"has-background\" style=\"background-color:#dff6ff;text-align:right;direction:rtl\"> <strong>\u0645\u0635\u0641\u0648\u0641\u0629 \u062c\u0627\u0643\u0648\u0628\u064a<\/strong> \u0647\u064a \u0645\u0635\u0641\u0648\u0641\u0629 \u0645\u0643\u0648\u0646\u0629 \u0645\u0646 \u0645\u0634\u062a\u0642\u0627\u062a \u062c\u0632\u0626\u064a\u0629 \u0645\u0646 \u0627\u0644\u062f\u0631\u062c\u0629 \u0627\u0644\u0623\u0648\u0644\u0649 \u0644\u0644\u062f\u0627\u0644\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0647\u064a \u0643\u0645\u0627 \u064a\u0644\u064a: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-de-la-matrice-jacobienne.webp\" alt=\"\u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629\" class=\"wp-image-2796\" width=\"477\" height=\"397\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0644\u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0645\u0635\u0641\u0648\u0641\u0627\u062a \u062c\u0627\u0643\u0648\u0628\u064a \u0633\u062a\u062d\u062a\u0648\u064a \u062f\u0627\u0626\u0645\u064b\u0627 \u0639\u0644\u0649 \u0639\u062f\u062f \u0645\u0646 \u0627\u0644\u0635\u0641\u0648\u0641 \u0645\u062b\u0644 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0639\u062f\u062f\u064a\u0629<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c2cded1f0c41f6c4f73404951209deec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(f_1,f_2,\\ldots ,f_m)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"114\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0644\u062f\u064a\u0643 \u0627\u0644\u0648\u0638\u064a\u0641\u0629\u060c \u0648\u0633\u0648\u0641 \u064a\u062a\u0648\u0627\u0641\u0642 \u0639\u062f\u062f \u0627\u0644\u0623\u0639\u0645\u062f\u0629 \u0645\u0639 \u0639\u062f\u062f \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-acf6e9bb52e3b1715802a12e9b93d938_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x_1, x_2, \\ldots , x_n).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"119\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u0646 \u0646\u0627\u062d\u064a\u0629 \u0623\u062e\u0631\u0649\u060c \u062a\u064f\u0639\u0631\u0641 \u0647\u0630\u0647 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0623\u064a\u0636\u064b\u0627 \u0628\u0627\u0644\u062e\u0631\u064a\u0637\u0629 <em>\u0627\u0644\u062a\u0641\u0627\u0636\u0644\u064a\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629<\/em> \u0623\u0648 <em>\u0627\u0644\u062e\u0631\u064a\u0637\u0629 \u0627\u0644\u062e\u0637\u064a\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629<\/em> . \u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639\u060c \u0623\u062d\u064a\u0627\u0646\u064b\u0627 \u064a\u062a\u0645 \u0643\u062a\u0627\u0628\u062a\u0647 \u0623\u064a\u0636\u064b\u0627 \u0628\u0627\u0644\u062d\u0631\u0641 D \u0628\u062f\u0644\u0627\u064b \u0645\u0646 \u0627\u0644\u062d\u0631\u0641 J:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a754eb7ba76edc6a0057255d4b17792c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle J_f = D_f\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"64\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0645\u0646 \u0628\u0627\u0628 \u0627\u0644\u0641\u0636\u0648\u0644\u060c \u062a\u0645 \u062a\u0633\u0645\u064a\u0629 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0639\u0644\u0649 \u0627\u0633\u0645 \u0643\u0627\u0631\u0644 \u063a\u0648\u0633\u062a\u0627\u0641 \u062c\u0627\u0643\u0648\u0628\u064a\u060c \u0648\u0647\u0648 \u0639\u0627\u0644\u0645 \u0631\u064a\u0627\u0636\u064a\u0627\u062a \u0648\u0623\u0633\u062a\u0627\u0630 \u0645\u0647\u0645 \u0641\u064a \u0627\u0644\u0642\u0631\u0646 \u0627\u0644\u062a\u0627\u0633\u0639 \u0639\u0634\u0631 \u0642\u062f\u0645 \u0645\u0633\u0627\u0647\u0645\u0627\u062a \u0645\u0647\u0645\u0629 \u0641\u064a \u0639\u0627\u0644\u0645 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0627\u062a\u060c \u0648\u062e\u0627\u0635\u0629 \u0641\u064a \u0645\u062c\u0627\u0644 \u0627\u0644\u062c\u0628\u0631 \u0627\u0644\u062e\u0637\u064a.<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0645\u062b\u0627\u0644 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629<\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0646\u0631\u0649 \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629\u060c \u0633\u0646\u0631\u0649 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628\u0647\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u062b\u0627\u0644:<\/p>\n<ul style=\";text-align:right;direction:rtl\">\n<li style=\";text-align:right;direction:rtl\"> \u062d\u062f\u062f \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 (1\u060c2) \u0644\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/li>\n<\/ul>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f0fc87451aa9fbec94159b7a916880c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x,y)= (x^4 +3y^2x \\ , \\ 5y^2-2xy+1)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"290\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0648\u0644 \u0634\u064a\u0621 \u064a\u062a\u0639\u064a\u0646 \u0639\u0644\u064a\u0646\u0627 \u0627\u0644\u0642\u064a\u0627\u0645 \u0628\u0647 \u0647\u0648 \u062d\u0633\u0627\u0628 \u062c\u0645\u064a\u0639 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u062c\u0632\u0626\u064a\u0629 \u0645\u0646 \u0627\u0644\u062f\u0631\u062c\u0629 \u0627\u0644\u0623\u0648\u0644\u0649 \u0644\u0644\u062f\u0627\u0644\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dec527bbc6852cbe54551e96000f8357_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial f_1}{\\partial x} = 4x^3+3y^2\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"124\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-65bf87809e33a1ea0113f875bf6d1187_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial f_1}{\\partial y} = 6yx\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"79\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6c8ed9d5e68e04f45efe36891a22c088_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial f_2}{\\partial x} = -2y\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"82\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-20a7a54e9162f3f423056d0638effb9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\cfrac{\\partial f_2}{\\partial y} = 10y-2x\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"118\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u0646\u0637\u0628\u0642 \u0635\u064a\u063a\u0629 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629. \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u062a\u062d\u062a\u0648\u064a \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0644\u0649 \u0645\u062a\u063a\u064a\u0631\u064a\u0646 \u0648\u062f\u0627\u0644\u062a\u064a\u0646 \u0639\u062f\u062f\u064a\u062a\u064a\u0646\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0633\u062a\u0643\u0648\u0646 \u0645\u0635\u0641\u0648\u0641\u0629 \u0645\u0631\u0628\u0639\u0629 \u0627\u0644\u0628\u0639\u062f 2\u00d72: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/matrice-jacobienne-22152-avec-deux-variables-et-2-fonctions-scalaires-1.webp\" alt=\"\" class=\"wp-image-2821\" width=\"504\" height=\"124\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629\u060c \u0646\u062d\u0633\u0628\u0647 \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 (1\u060c2):<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fa6ed35890b94e3abe43b9a3f9674e36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle J_f(1,2)=\\begin{pmatrix} 4\\cdot 1^3+3\\cdot 2^2 &amp; 6\\cdot 2 \\cdot 1 \\\\[3ex] -2\\cdot 2 &amp; 10\\cdot 2-2 \\cdot 1 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"313\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627 \u0646\u0642\u0648\u0645 \u0628\u062a\u0646\u0641\u064a\u0630 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0648\u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0627\u0644\u062d\u0644: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-calcul-de-la-matrice-jacobienne.webp\" alt=\"\u0645\u062b\u0627\u0644 \u0644\u062d\u0633\u0627\u0628 \u0645\u0635\u0641\u0648\u0641\u0629 \u062c\u0627\u0643\u0648\u0628\u064a\" class=\"wp-image-2823\" width=\"209\" height=\"71\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u062a\u0639\u0631\u0641\u062a \u0639\u0644\u0649 \u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629\u060c \u0646\u062a\u0631\u0643 \u0644\u0643 \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u062d\u062a\u0649 \u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u064a\u0647\u0627.<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u062d\u0644 \u0645\u0633\u0627\u0626\u0644 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629<\/h2>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 1<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0623\u0648\u062c\u062f \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 (0,-2) \u0644\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0645\u062a\u062c\u0647\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0641\u064a \u0645\u062a\u063a\u064a\u0631\u064a\u0646: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-210a9fdec3d1430dd17f52f91fb8a5fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x,y)= (e^{xy}+y \\ , \\ y^2x)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"190\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u062a\u062d\u062a\u0648\u064a \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0644\u0649 \u0645\u062a\u063a\u064a\u0631\u064a\u0646 \u0648\u062f\u0648\u0627\u0644\u062a\u064a\u0646 \u0639\u062f\u062f\u064a\u062a\u064a\u0646\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0633\u062a\u0643\u0648\u0646 \u0645\u0635\u0641\u0648\u0641\u0629 \u0645\u0631\u0628\u0639\u0629 \u0628\u062d\u062c\u0645 2\u00d72: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-de-la-matrice-jacobienne.webp\" alt=\"\u062d\u0644 \u062a\u0645\u0631\u064a\u0646 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629\" class=\"wp-image-2840\" width=\"511\" height=\"124\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0646\u062d\u0633\u0628 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062e\u0627\u0635 \u0628\u0645\u0635\u0641\u0648\u0641\u0629 \u062c\u0627\u0643\u0648\u0628\u064a\u060c \u0646\u0642\u064a\u0645\u0647 \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 (0\u060c-2):<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f6008d8799a0a1c3a667e958d6c8818_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle J_f(0,-2)=\\begin{pmatrix}e^{0\\cdot (-2)}\\cdot (-2)\\phantom{5} &amp; \\phantom{5}e^{0\\cdot (-2)} \\cdot 0 +1 \\\\[4ex](-2)^2 &amp; 2\\cdot (-2) \\cdot 0 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"75\" width=\"352\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u0627 \u0646\u0642\u0648\u0645 \u0628\u062a\u0646\u0641\u064a\u0630 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0648\u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0627\u0644\u0646\u062a\u064a\u062c\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5eb37dc494497a424b489235b1a55a5f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{J_f(0,-2)}=\\begin{pmatrix} \\bm{-2} &amp; \\bm{1} \\\\[1.5ex] \\bm{4} &amp; \\bm{0} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"166\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u062a\u0645\u0631\u064a\u0646 2<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u062d\u0633\u0628 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 (2\u060c-1) \u0644\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0628\u0645\u062a\u063a\u064a\u0631\u064a\u0646: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cf0b9acb2545e2e42f1e63a0edb5a7c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x,y)= (x^3y^2 - 5x^2y^2 \\ , \\ y^6-3y^3x+7)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"314\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u062a\u062d\u062a\u0648\u064a \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0644\u0649 \u0645\u062a\u063a\u064a\u0631\u064a\u0646 \u0648\u062f\u0648\u0627\u0644\u062a\u064a\u0646 \u0639\u062f\u062f\u064a\u062a\u064a\u0646\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0645\u0635\u0641\u0648\u0641\u0629 \u062c\u0627\u0643\u0648\u0628\u064a \u0633\u062a\u0643\u0648\u0646 \u0645\u0635\u0641\u0648\u0641\u0629 \u0645\u0631\u0628\u0639\u0629 \u0645\u0646 \u0627\u0644\u0631\u062a\u0628\u0629 2:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-48baf447fc5a448f30f13295f96cb874_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle J_f(x,y)=\\begin{pmatrix}\\cfrac{\\phantom{5}\\partial f_1}{\\partial x}\\phantom{5} &amp; \\phantom{5}\\cfrac{\\partial f_1}{\\partial y}\\phantom{5} \\\\[3ex] \\cfrac{\\partial f_2}{\\partial x} &amp; \\cfrac{\\partial f_2}{\\partial y}\\end{pmatrix} = \\begin{pmatrix} \\vphantom{\\cfrac{\\partial f_2}{\\partial x}}3x^2y^2-10xy^2&amp; 2x^3y-10x^2y \\\\[3ex] \\vphantom{\\cfrac{\\partial f_2}{\\partial x}} -3y^3 &amp; 6y^5-9y^2x \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"101\" width=\"502\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0628\u0645\u062c\u0631\u062f \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062e\u0627\u0635 \u0628\u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629\u060c \u0646\u062d\u0633\u0628\u0647 \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 (2\u060c-1):<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f2ee2de8e72eed6956f784628353547_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle J_f(2,-1)=\\begin{pmatrix} 3\\cdot 2^2\\cdot (-1)^2-10\\cdot 2 \\cdot (-1)^2\\phantom{5} &amp; \\phantom{5}2\\cdot 2^3\\cdot (-1)-10\\cdot 2^2\\cdot (-1) \\\\[4ex] -3(-1)^3 &amp; 6\\cdot (-1)^5-9\\cdot (-1)^2\\cdot 2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"74\" width=\"573\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u0627 \u0646\u0642\u0648\u0645 \u0628\u062a\u0646\u0641\u064a\u0630 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0648\u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0627\u0644\u0646\u062a\u064a\u062c\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7935318698eadf3d3af4f87e6e8f2629_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{J_f(1,2)}=\\begin{pmatrix} \\bm{-8} &amp; \\bm{24} \\\\[1.5ex] \\bm{3} &amp; \\bm{-24} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"175\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u0627\u0644\u062a\u0645\u0631\u064a\u0646 3<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u062f\u062f \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 (2\u060c-2\u060c2) \u0644\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0628\u062b\u0644\u0627\u062b\u0629 \u0645\u062a\u063a\u064a\u0631\u0627\u062a: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d63b0e9c8ecd37b9f100a46233ef9d48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x,y,z)= \\left(z\\tan (x^2-y^2) \\ , \\ xy\\ln \\left( \\frac{z}{2} \\right)\\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"313\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u062a\u062d\u062a\u0648\u064a \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0644\u0649 \u062b\u0644\u0627\u062b\u0629 \u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0648\u062f\u0627\u0644\u062a\u064a\u0646 \u0639\u062f\u062f\u064a\u062a\u064a\u0646\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0633\u062a\u0643\u0648\u0646 \u0645\u0635\u0641\u0648\u0641\u0629 \u0645\u0633\u062a\u0637\u064a\u0644\u0629 \u0627\u0644\u0628\u0639\u062f 2\u00d73: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5b327537a2e4c80c7eb38d56d94bb141_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle J_f(x,y,z)= \\begin{pmatrix}\\cfrac{\\phantom{5}\\partial f_1}{\\partial x}\\phantom{5} &amp; \\phantom{5}\\cfrac{\\partial f_1}{\\partial y}\\phantom{5} &amp; \\phantom{5}\\cfrac{\\partial f_1}{\\partial z}\\phantom{5} \\\\[3ex] \\cfrac{\\partial f_2}{\\partial x} &amp; \\cfrac{\\partial f_2}{\\partial y} &amp;\\cfrac{\\partial f_2}{\\partial z}\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"101\" width=\"297\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-de-la-matrice-jacobienne-resolu-avec-3-variables.webp\" alt=\"\u062d\u0644 \u062a\u0645\u0631\u064a\u0646 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0644\u062b\u0644\u0627\u062b\u0629 \u0645\u062a\u063a\u064a\u0631\u0627\u062a\" class=\"wp-image-2870\" width=\"798\" height=\"121\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0627\u0644\u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u062e\u0627\u0635 \u0628\u0645\u0635\u0641\u0648\u0641\u0629 \u062c\u0627\u0643\u0648\u0628\u064a\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u062d\u0633\u0628\u0647 \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 (2\u060c-2\u060c2):<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a62dd1b4655e9d089404028ec48fbe11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle J_f(2,-2,2)= \\begin{pmatrix} \\vphantom{\\cfrac{\\partial f_2}{\\partial x}}2\\bigl(1+\\tan^2 (2^2-(-2)^2)\\bigr) \\cdot 2\\cdot 2 &amp; 2\\bigl(1+\\tan^2 (2^2-(-2)^2)\\bigr) \\cdot (-2\\cdot (-2)) &amp; \\tan (2^2-(-2)^2)\\\\[3ex] \\vphantom{\\cfrac{\\partial f_2}{\\partial x}} \\displaystyle -2\\ln \\left( \\frac{2}{2} \\right) &amp; \\displaystyle 2\\ln \\left( \\frac{2}{2} \\right) &amp;\\displaystyle \\frac{2\\cdot (-2)}{2} \\right)\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"106\" width=\"804\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0642\u0648\u0645 \u0628\u0625\u062c\u0631\u0627\u0621 \u0627\u0644\u062d\u0633\u0627\u0628\u0627\u062a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-05c8aaa8cca0f4cb652c95b11d2e9db1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle J_f(2,-2,2)= \\begin{pmatrix} \\vphantom{\\cfrac{\\partial f_2}{\\partial x}}2\\bigl(1+\\tan^2 (0)\\bigr) \\cdot 4 \\phantom{5} &amp; 2\\bigl(1+\\tan^2 (0)\\bigr) \\cdot 4 &amp; \\phantom{5}\\tan (0)\\\\[3ex] \\vphantom{\\cfrac{\\partial f_2}{\\partial x}} -2\\cdot 0 &amp;  2\\cdot 0 &amp;-2 \\right)\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"95\" width=\"506\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0646\u062d\u0646 \u0646\u0648\u0627\u0635\u0644 \u0627\u0644\u0639\u0645\u0644 \u062d\u062a\u0649 \u0644\u0645 \u064a\u0639\u062f \u0645\u0646 \u0627\u0644\u0645\u0645\u0643\u0646 \u062a\u0628\u0633\u064a\u0637\u0647: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d2b4fda9837a6287456ca469d46a2382_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{J_f(2,-2,2)=} \\begin{pmatrix}\\bm{8} &amp; \\bm{8} &amp; \\bm{0} \\\\[2ex]   \\bm{0} &amp; \\bm{0} &amp;\\bm{-2} \\right)\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"64\" width=\"208\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<div class=\"adsb30\" style=\" margin:px; text-align:;text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u062a\u0645\u0631\u064a\u0646 4<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0639\u0646\u062f \u0647\u0630\u0647 \u0627\u0644\u0646\u0642\u0637\u0629<strong> <\/strong><\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-636bdeb4752c0344a75d5969fb84917a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\pi, \\pi)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"41\" style=\"vertical-align: -5px;\"><\/p>\n<p>\u0644\u0644\u0648\u0638\u064a\u0641\u0629 \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062a\u0627\u0644\u064a\u0629: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a9b36f1402d71e330215cbee0169a58f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x,y)= \\left( \\frac{\\cos (x-y)}{x} \\ , \\ e^{x^2-y^2} \\ , \\ x^3\\sin (2y) \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"343\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u062a\u062d\u062a\u0648\u064a \u0627\u0644\u062f\u0627\u0644\u0629 \u0639\u0644\u0649 \u0645\u062a\u063a\u064a\u0631\u064a\u0646 \u0648\u062b\u0644\u0627\u062b \u062f\u0648\u0627\u0644 \u0639\u062f\u062f\u064a\u0629\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0633\u062a\u0643\u0648\u0646 \u0645\u0635\u0641\u0648\u0641\u0629 \u0645\u0633\u062a\u0637\u064a\u0644\u0629 \u0627\u0644\u0628\u0639\u062f 3\u00d72: <\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-etape-par-etape-de-jacobian-matrix-32152-1.webp\" alt=\"\u062a\u0645\u0631\u064a\u0646 \u062a\u0645 \u062d\u0644\u0647 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u062c\u0627\u0643\u0648\u0628\u064a\" class=\"wp-image-2886\" width=\"704\" height=\"192\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0628\u0645\u062c\u0631\u062f \u0623\u0646 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u062a\u0639\u0628\u064a\u0631 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u0648\u062c\u062f \u0642\u064a\u0645\u0629 \u0647\u0630\u0647 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fbf56ffad010b2211cd457a72a08d870_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(\\pi, \\pi):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-167caa7a7d1cb34db33f7b92e21b5f78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle J_f(\\pi,\\pi)= \\begin{pmatrix} \\displaystyle \\vphantom{\\cfrac{\\partial f_3}{\\partial y}}\\frac{-\\sin(\\pi-\\pi)\\pi-\\cos(\\pi-\\pi)}{\\pi^2} &amp; \\displaystyle\\frac{\\sin (\\pi- \\pi)}{\\pi} \\\\[3ex] \\vphantom{\\cfrac{\\partial f_3}{\\partial y}}2\\pi e^{\\pi^2-\\pi^2} &amp; -2\\pi e^{\\pi^2-\\pi^2} \\\\[3ex] \\vphantom{\\cfrac{\\partial f_3}{\\partial y}} 3\\pi^2\\sin(2\\pi) &amp; \\pi^3 \\cos(2\\pi)\\cdot 2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"159\" width=\"440\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u0642\u0648\u0645 \u0628\u062a\u0646\u0641\u064a\u0630 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b05c5bfee3f874f3adec324a6bc9b43e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle J_f(\\pi,\\pi)= \\begin{pmatrix} \\displaystyle \\vphantom{\\cfrac{\\partial f_3}{\\partial y}}\\displaystyle\\frac{-0-1}{\\pi^2} &amp; \\displaystyle\\frac{0}{\\pi} \\\\[3ex] \\vphantom{\\cfrac{\\partial f_3}{\\partial y}}2\\pi e^{0} &amp; -2\\pi e^{0} \\\\[3ex] \\vphantom{\\cfrac{\\partial f_3}{\\partial y}} 3\\pi^2\\cdot 0 &amp; \\pi^3 \\cdot 1 \\cdot 2 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"159\" width=\"246\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0644\u0648\u0638\u064a\u0641\u0629 \u0627\u0644\u0645\u062a\u062c\u0647 \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 \u0642\u064a\u062f \u0627\u0644\u0646\u0638\u0631 \u062a\u0633\u062a\u062d\u0642: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f4addee61e4664b95dbb049be217af34_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{J_f(\\pi,\\pi)=} \\begin{pmatrix}\\displaystyle -\\frac{\\bm{1}}{\\bm{\\pi^2}} &amp; \\bm{0} \\\\[3ex] \\bm{2\\pi} &amp; \\bm{-2\\pi}\\\\[3ex]\\bm{0} &amp; \\bm{2\\pi^3} \\right)\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"119\" width=\"195\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\">\u0627\u0644\u062a\u0645\u0631\u064a\u0646 5<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u062d\u0633\u0628 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0639\u0646\u062f \u0647\u0630\u0647 \u0627\u0644\u0646\u0642\u0637\u0629<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-31e57c38165a2810230c0ca075aefde9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3,0,\\pi)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -5px;\"><\/p>\n<p> \u0644\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629 \u0645\u0639 3 \u0645\u062a\u063a\u064a\u0631\u0627\u062a: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d7841aa7ac90f968d460391c8d1529ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x,y,z)= \\left(xe^{2y}\\cos(-z) \\ , \\ (y-2)^3\\cdot \\sin\\left(\\frac{z}{2}\\right)  \\ , \\ e^{2y}\\cdot \\ln\\left(\\frac{x}{3}\\right) \\right)\" title=\"Rendered by QuickLaTeX.com\" height=\"33\" width=\"472\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E3F2FD boto_ver_solucion\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E3F2FD\" style=\"text-align:center;text-align:right;direction:rtl\">\n<div class=\"otfm-sp__title\" style=\";text-align:right;direction:rtl\"> <strong>\u0627\u0646\u0638\u0631 \u0627\u0644\u062d\u0644<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u062a\u0643\u0648\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u0645\u0643\u0648\u0646\u0629 \u0645\u0646 \u062b\u0644\u0627\u062b\u0629 \u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0648\u062b\u0644\u0627\u062b \u062f\u0648\u0627\u0644 \u0639\u062f\u062f\u064a\u0629\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0641\u0625\u0646 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0633\u062a\u0643\u0648\u0646 \u0645\u0635\u0641\u0648\u0641\u0629 \u0645\u0631\u0628\u0639\u0629 \u0627\u0644\u0628\u0639\u062f 3\u00d73: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bfd9dcbb1d4961906d5b8581f70f5392_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle J_f(x,y,z)=\\begin{pmatrix}\\phantom{5}\\cfrac{\\partial f_1}{\\partial x}\\phantom{5} &amp; \\phantom{5}\\cfrac{\\partial f_1}{\\partial y}\\phantom{5} &amp; \\phantom{5}\\cfrac{\\partial f_1}{\\partial z}\\phantom{5} \\\\[3ex] \\cfrac{\\partial f_2}{\\partial x} &amp; \\cfrac{\\partial f_2}{\\partial y} &amp; \\cfrac{\\partial f_2}{\\partial z} \\\\[3ex] \\cfrac{\\partial f_3}{\\partial x} &amp; \\cfrac{\\partial f_3}{\\partial y} &amp; \\cfrac{\\partial f_3}{\\partial z}\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"161\" width=\"297\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-image\" style=\";text-align:right;direction:rtl\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exercice-resolu-de-la-matrice-jacobienne-32153-avec-3-variables.webp\" alt=\"\u062d\u0644 \u062a\u0645\u0631\u064a\u0646 \u0644\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 3\u00d73 \u0645\u0639 3 \u0645\u062a\u063a\u064a\u0631\u0627\u062a\" class=\"wp-image-2937\" width=\"629\" height=\"191\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0628\u0645\u062c\u0631\u062f \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0645\u0635\u0641\u0648\u0641\u0629 \u062c\u0627\u0643\u0648\u0628\u064a\u060c \u0646\u0642\u064a\u0645\u0647\u0627 \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-696ca943dc60b9e55cbc96d72e3c0c19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(3,0,\\pi):\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4f56df32b7632d1e74f014f0aab2b52a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle J_f(3,0,\\pi)= \\begin{pmatrix} \\vphantom{\\cfrac{\\partial f_2}{\\partial x}} e^{2\\cdot 0}\\cos(-\\pi) &amp; 2\\cdot 3e^{2\\cdot 0}\\cos(-\\pi) &amp; 3e^{2\\cdot 0}\\sin(-\\pi) \\\\[3ex] \\vphantom{\\cfrac{\\partial f_2}{\\partial x}} 0 &amp; \\displaystyle 3(0-2)^2\\cdot \\sin\\left(\\frac{\\pi}{2}\\right) &amp; \\displaystyle\\frac{1}{2}(0-2)^3\\cdot \\cos\\left(\\frac{\\pi}{2}\\right)\\\\[3ex] \\vphantom{\\cfrac{\\partial f_2}{\\partial x}}\\displaystyle\\frac{e^{2\\cdot 0}}{3} &amp;\\displaystyle 2e^{2\\cdot 0}\\cdot \\ln\\left(\\frac{3}{3}\\right) &amp; 0\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"162\" width=\"542\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0633\u0628 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5771c5e1c54eabf6df6633abd5f3e194_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle J_f(3,0,\\pi)= \\begin{pmatrix} \\vphantom{\\cfrac{\\partial f_2}{\\partial x}} 1\\cdot (-1) &amp; 6\\cdot 1\\cdot (-1) &amp; 3\\cdot 1 \\cdot 0 \\\\[3ex] \\vphantom{\\cfrac{\\partial f_2}{\\partial x}} 0 &amp; \\displaystyle 3\\cdot 4 \\cdot 1 &amp; \\displaystyle\\frac{1}{2}\\cdot (-8)\\cdot 0\\\\[3ex] \\vphantom{\\cfrac{\\partial f_2}{\\partial x}}\\displaystyle\\frac{1}{3} &amp;\\displaystyle 2\\cdot 1\\cdot  0 &amp; 0\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"159\" width=\"380\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0646\u062a\u064a\u062c\u0629 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0639\u0646\u062f \u0647\u0630\u0647 \u0627\u0644\u0646\u0642\u0637\u0629 \u0647\u064a: <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6dc1884b96ce985e1475c5cfcba2fff8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\bm{J_f(3,0,\\pi)=} \\begin{pmatrix} \\vphantom{\\cfrac{\\partial f_2}{\\partial x}} \\bm{-1} &amp; \\bm{-6} &amp; \\phantom{-}\\bm{0} \\\\[2ex]  \\bm{0} &amp; \\bm{12} &amp; \\displaystyle \\bm{0} \\\\[2ex] \\displaystyle \\frac{\\bm{1}}{\\bm{3}} &amp;\\bm{0}&amp; \\bm{0}\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"121\" width=\"224\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\" style=\";text-align:right;direction:rtl\"><\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center;text-align:right;direction:rtl\">\n<div id=\"ezoic-pub-ad-placeholder-118\" style=\";text-align:right;direction:rtl\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0645\u062d\u062f\u062f \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629: \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629<\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0645\u062d\u062f\u062f \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u064a\u0633\u0645\u0649 \u0627\u0644\u0645\u062d\u062f\u062f <strong>\u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a<\/strong> \u0623\u0648 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a. \u064a\u062c\u0628 \u0623\u0646 \u064a\u0624\u062e\u0630 \u0641\u064a \u0627\u0644\u0627\u0639\u062a\u0628\u0627\u0631 \u0623\u0646\u0647 \u0644\u0627 \u064a\u0645\u0643\u0646 \u062d\u0633\u0627\u0628 \u062f\u0627\u0644\u0629 \u062c\u0627\u0643\u0648\u0628\u064a \u0625\u0644\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u062f\u0627\u0644\u0629 \u062a\u062d\u062a\u0648\u064a \u0639\u0644\u0649 \u0646\u0641\u0633 \u0639\u062f\u062f \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0645\u062b\u0644 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0639\u062f\u062f\u064a\u0629\u060c \u0644\u0623\u0646 \u0645\u0635\u0641\u0648\u0641\u0629 \u062c\u0627\u0643\u0648\u0628\u064a \u0633\u062a\u0643\u0648\u0646 \u0644\u0647\u0627 \u0646\u0641\u0633 \u0639\u062f\u062f \u0627\u0644\u0635\u0641\u0648\u0641 \u0645\u062b\u0644 \u0627\u0644\u0623\u0639\u0645\u062f\u0629\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0633\u062a\u0643\u0648\u0646 \u0645\u0631\u0628\u0639\u064b\u0627 \u0645\u0635\u0641\u0648\u0641\u0629. .<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0645\u062b\u0627\u0644 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u062f\u0639\u0648\u0646\u0627 \u0646\u0631\u0649 \u0645\u062b\u0627\u0644\u0627\u064b \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u062d\u062f\u062f \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a \u0644\u062f\u0627\u0644\u0629 \u0630\u0627\u062a \u0645\u062a\u063a\u064a\u0631\u064a\u0646:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a23f671a7521885bf05872fbc353e7fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x,y)= (x^2-y^2 \\ , \\ 2xy)\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"193\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0646\u062d\u0633\u0628 \u0623\u0648\u0644\u0627\u064b \u0645\u0635\u0641\u0648\u0641\u0629 \u062c\u0627\u0643\u0648\u0628\u064a \u0644\u0644\u062f\u0627\u0644\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5870e75f368ea3e554b2fa32cfa554dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle J_f(x,y)=\\begin{pmatrix}\\cfrac{\\phantom{5}\\partial f_1}{\\partial x}\\phantom{5} &amp; \\phantom{5}\\cfrac{\\partial f_1}{\\partial y}\\phantom{5} \\\\[3ex] \\cfrac{\\partial f_2}{\\partial x} &amp; \\cfrac{\\partial f_2}{\\partial y}\\end{pmatrix} = \\begin{pmatrix} \\vphantom{\\cfrac{\\partial f_2}{\\partial x}}2x \\phantom{5}&amp; -2y \\\\[2ex] \\vphantom{\\cfrac{\\partial f_2}{\\partial x}} 2y &amp; 2x \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"101\" width=\"349\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\" style=\";text-align:right;direction:rtl\"> \u0648\u0627\u0644\u0622\u0646 \u0646\u062d\u0644 \u0645\u062d\u062f\u062f \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 2\u00d72:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6d1ef9df1d4735e3cea235c653714439_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{det}\\bigl(J_f(x,y)\\bigr) =\\begin{vmatrix} 2x&amp;-2y \\\\[2ex] 2y &amp; 2x \\end{vmatrix} = \\bm{4x^2+4y^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"300\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a \u0648\u0627\u0646\u0639\u0643\u0627\u0633 \u0627\u0644\u0648\u0638\u064a\u0641\u0629<\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0622\u0646 \u0628\u0639\u062f \u0623\u0646 \u0631\u0623\u064a\u062a \u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u060c \u0631\u0628\u0645\u0627 \u0641\u0643\u0631\u062a&#8230; \u062d\u0633\u0646\u064b\u0627\u060c \u0645\u0627 \u0627\u0644\u0645\u063a\u0632\u0649 \u0645\u0646 \u0630\u0644\u0643\u061f<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u0633\u0646\u064b\u0627\u060c \u0627\u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0631\u0626\u064a\u0633\u064a \u0644\u0644\u062c\u0627\u0643\u0648\u0628\u064a\u0627\u0646 \u0647\u0648 \u062a\u062d\u062f\u064a\u062f \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0645\u0646 \u0627\u0644\u0645\u0645\u0643\u0646 \u0639\u0643\u0633 \u0627\u0644\u062f\u0627\u0644\u0629. \u062a\u0642\u0648\u0644 <strong>\u0646\u0638\u0631\u064a\u0629 \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0639\u0643\u0633\u064a\u0629<\/strong> \u0623\u0646\u0647 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0645\u062d\u062f\u062f \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 (\u0627\u0644\u062c\u0627\u0643\u0648\u0628\u064a\u0629) \u064a\u062e\u062a\u0644\u0641 \u0639\u0646 0\u060c \u0641\u0647\u0630\u0627 \u064a\u0639\u0646\u064a \u0623\u0646 \u0647\u0630\u0647 \u0627\u0644\u062f\u0627\u0644\u0629 \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u0639\u0643\u0633.<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d719077544284d291fe9faf0fbf0a099_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\text{det}\\bigl(J_f\\bigr) \\neq 0 \\ \\longrightarrow \\ \\exists \\ f^{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"186\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062a\u062c\u062f\u0631 \u0627\u0644\u0625\u0634\u0627\u0631\u0629 \u0625\u0644\u0649 \u0623\u0646 \u0647\u0630\u0627 \u0627\u0644\u0634\u0631\u0637 \u0636\u0631\u0648\u0631\u064a \u0648\u0644\u0643\u0646\u0647 \u063a\u064a\u0631 \u0643\u0627\u0641\u060c \u0623\u064a \u0623\u0646\u0647 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u062d\u062f\u062f \u063a\u064a\u0631 \u0635\u0641\u0631 \u0641\u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u062c\u0632\u0645 \u0628\u0623\u0646 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u064a\u0645\u0643\u0646 \u0642\u0644\u0628\u0647\u0627\u060c \u0623\u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u062d\u062f\u062f 0 \u0641\u0644\u0627 \u064a\u0645\u0643\u0646\u0646\u0627 \u0645\u0639\u0631\u0641\u0629 \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u0645\u062d\u062f\u062f \u0647\u0648 \u0635\u0641\u0631 \u0623\u0645 \u0644\u0627. \u0627\u0644\u062f\u0627\u0644\u0629 \u0644\u0647\u0627 \u0645\u0639\u0643\u0648\u0633 \u0623\u0648 \u0644\u0627<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0641\u064a \u0627\u0644\u0645\u062b\u0627\u0644 \u0627\u0644\u0630\u064a \u0631\u0623\u064a\u0646\u0627\u0647 \u0633\u0627\u0628\u0642\u064b\u0627 \u062d\u0648\u0644 \u0643\u064a\u0641\u064a\u0629 \u0627\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a \u0644\u0644\u062f\u0627\u0644\u0629\u060c \u0641\u0625\u0646 \u0627\u0644\u0645\u062d\u062f\u062f \u064a\u0639\u0637\u064a<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f2387cef5f9f9d4963e2e311bd672bfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4x^2+4y^2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -4px;\"><\/p>\n<p> . \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629 \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0644\u062c\u0632\u0645 \u0628\u0623\u0646 \u0627\u0644\u062f\u0627\u0644\u0629 \u064a\u0645\u0643\u0646 \u062f\u0627\u0626\u0645\u0627 \u0623\u0646 \u062a\u0643\u0648\u0646 \u0645\u0639\u0643\u0648\u0633\u0629 \u0625\u0644\u0627 \u0639\u0646\u062f \u0627\u0644\u0646\u0642\u0637\u0629 (0,0)\u060c \u062d\u064a\u062b \u0623\u0646 \u0647\u0630\u0647 \u0627\u0644\u0646\u0642\u0637\u0629 \u0647\u064a \u0627\u0644\u0648\u062d\u064a\u062f\u0629 \u0627\u0644\u062a\u064a \u064a\u0633\u0627\u0648\u064a \u0641\u064a\u0647\u0627 \u0627\u0644\u0645\u062d\u062f\u062f \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a \u0627\u0644\u0635\u0641\u0631\u060c \u0648\u0628\u0627\u0644\u062a\u0627\u0644\u064a \u0644\u0627 \u0646\u0639\u0631\u0641 \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u0639\u0643\u0633\u064a\u0629 \u0623\u0645 \u0644\u0627 \u0645\u0648\u062c\u0648\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0646\u0642\u0637\u0629. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center;text-align:right;direction:rtl\">\n<div id=\"ezoic-pub-ad-placeholder-119\" style=\";text-align:right;direction:rtl\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0628\u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0623\u062e\u0631\u0649<\/h2>\n<p style=\";text-align:right;direction:rtl\"> \u062a\u0631\u062a\u0628\u0637 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0628\u0627\u0644\u062a\u062f\u0631\u062c \u0648\u0645\u0635\u0641\u0648\u0641\u0629 \u0647\u0633\u0647 \u0644\u0644\u062f\u0627\u0644\u0629:<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0645\u064a\u0644<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u062f\u0627\u0644\u0629 \u062f\u0627\u0644\u0629 \u0639\u062f\u062f\u064a\u0629\u060c \u0641\u0633\u062a\u0643\u0648\u0646 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0639\u0628\u0627\u0631\u0629 \u0639\u0646 \u0645\u0635\u0641\u0648\u0641\u0629 \u0635\u0641\u064a\u0629 \u0648\u0627\u0644\u062a\u064a \u0633\u062a\u0643\u0648\u0646 \u0645\u0643\u0627\u0641\u0626\u0629 <strong>\u0644\u0644\u062a\u062f\u0631\u062c<\/strong> : <\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c493f1d8b149a2ed4710288031d7be71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f: \\mathbb{R}^n \\to \\mathbb{R}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-278699b80ce58cadb5c056b945483637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle J_f = \\nabla f = \\begin{pmatrix}\\phantom{5} \\cfrac{\\partial f}{\\partial x_1} \\phantom{5}&amp; \\cfrac{\\partial f}{\\partial x_2}&amp; \\dots &amp; \\cfrac{\\partial f}{\\partial x_n}\\phantom{5} \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"304\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u0645\u0635\u0641\u0648\u0641\u0629 \u0647\u0633\u0647<\/h3>\n<p style=\";text-align:right;direction:rtl\"> \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0644\u062a\u062f\u0631\u062c \u0627\u0644\u062f\u0627\u0644\u0629 \u062a\u0633\u0627\u0648\u064a <strong>\u0645\u0635\u0641\u0648\u0641\u0629 \u0647\u0633\u0647<\/strong> :<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-96ab1054f3c447eedac17f9ce04b4606_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle H_f = J(\\nabla f)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"97\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062a\u0639\u062a\u0628\u0631 \u0627\u0644\u0647\u0633\u064a \u0645\u0635\u0641\u0648\u0641\u0629 \u0645\u0647\u0645\u0629 \u062c\u062f\u0627\u064b \u0644\u0627\u0634\u062a\u0642\u0627\u0642 \u0627\u0644\u062f\u0648\u0627\u0644 \u0630\u0627\u062a \u0623\u0643\u062b\u0631 \u0645\u0646 \u0645\u062a\u063a\u064a\u0631\u060c \u0644\u0623\u0646\u0647\u0627 \u062a\u062a\u0643\u0648\u0646 \u0645\u0646 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u062b\u0627\u0646\u064a\u0629 \u0644\u0644\u062f\u0627\u0644\u0629. \u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639\u060c \u064a\u0645\u0643\u0646 \u0644\u0644\u0645\u0631\u0621 \u0623\u0646 \u064a\u0642\u0648\u0644 \u0623\u0646 <a href=\"https:\/\/mathority.org\/ar\/\u0645\u0635\u0641\u0648\u0641\u0629-\u0647\u0633\u0647-\u0647\u0633\u0647-2x2-3x3\/\">\u0645\u0635\u0641\u0648\u0641\u0629 \u0647\u0633\u0647<\/a> \u0647\u064a \u0627\u0633\u062a\u0645\u0631\u0627\u0631\u064a\u0629 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629. \u0648\u0644\u0643\u0646 \u0645\u0646 \u0627\u0644\u0645\u0647\u0645 \u062c\u062f\u064b\u0627 \u0623\u0646 \u064a\u0643\u0648\u0646 \u0644\u062f\u064a\u0646\u0627 \u0635\u0641\u062d\u0629 \u0643\u0627\u0645\u0644\u0629 \u062a\u0634\u0631\u062d \u0630\u0644\u0643 \u0628\u0627\u0644\u062a\u0641\u0635\u064a\u0644. \u0644\u0630\u0644\u0643\u060c \u0625\u0630\u0627 \u0643\u0646\u062a \u062a\u0631\u064a\u062f \u0623\u0646 \u062a\u0639\u0631\u0641 \u0628\u0627\u0644\u0636\u0628\u0637 \u0645\u0627 \u0647\u064a \u0647\u0630\u0647 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0648\u0644\u0645\u0627\u0630\u0627 \u0647\u064a \u0645\u0645\u064a\u0632\u0629 \u062c\u062f\u064b\u0627\u060c \u064a\u0645\u0643\u0646\u0643 \u0627\u0644\u0646\u0642\u0631 \u0641\u0648\u0642 \u0627\u0644\u0631\u0627\u0628\u0637.<\/p>\n<h2 class=\"wp-block-heading\" style=\";text-align:right;direction:rtl\"> \u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0639\u0644\u0649 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629<\/h2>\n<div class=\"adsb30\" style=\" margin:px; text-align:;text-align:right;direction:rtl\"><\/div>\n<p style=\";text-align:right;direction:rtl\"> \u0625\u0644\u0649 \u062c\u0627\u0646\u0628 \u0627\u0644\u0641\u0627\u0626\u062f\u0629 \u0627\u0644\u062a\u064a \u0631\u0623\u064a\u0646\u0627\u0647\u0627 \u0645\u0646 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629\u060c \u0648\u0627\u0644\u062a\u064a \u062a\u062d\u062f\u062f \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u062f\u0627\u0644\u0629 \u0642\u0627\u0628\u0644\u0629 \u0644\u0644\u0639\u0643\u0633\u060c \u0641\u0625\u0646 \u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u062c\u0627\u0643\u0648\u0628\u064a \u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0623\u062e\u0631\u0649.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0635\u0641\u0648\u0641\u0629 \u062c\u0627\u0643\u0648\u0628\u064a \u0644\u062d\u0633\u0627\u0628 <strong><span style=\"color:#1976d2;\">\u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u062d\u0631\u062c\u0629<\/span><\/strong> \u0644\u0644\u062f\u0627\u0644\u0629 \u0645\u062a\u0639\u062f\u062f\u0629 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a\u060c \u0648\u0627\u0644\u062a\u064a \u064a\u062a\u0645 \u062a\u0635\u0646\u064a\u0641\u0647\u0627 \u0628\u0639\u062f \u0630\u0644\u0643 \u0625\u0644\u0649 \u0646\u0642\u0627\u0637 \u0639\u0638\u0645\u0649 \u0623\u0648 \u0635\u063a\u0631\u0649 \u0623\u0648 \u0646\u0642\u0627\u0637 \u0633\u0631\u062c \u0645\u0646 \u062e\u0644\u0627\u0644 \u0645\u0635\u0641\u0648\u0641\u0629 \u0647\u0633\u0647. \u0644\u0644\u0639\u062b\u0648\u0631 \u0639\u0644\u0649 \u0627\u0644\u0646\u0642\u0627\u0637 \u0627\u0644\u062d\u0631\u062c\u0629\u060c \u062a\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u062d\u0633\u0627\u0628 \u0645\u0635\u0641\u0648\u0641\u0629 \u062c\u0627\u0643\u0648\u0628\u064a \u0644\u0644\u062f\u0627\u0644\u0629\u060c \u0648\u062a\u0633\u0648\u064a\u062a\u0647\u0627 \u0628\u0627\u0644\u0635\u0641\u0631\u060c \u0648\u062d\u0644 \u0627\u0644\u0645\u0639\u0627\u062f\u0644\u0627\u062a \u0627\u0644\u0646\u0627\u062a\u062c\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d0c053381fc5f78d85944f3f431e5537_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle J_f(x)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"74\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u064a\u0648\u062c\u062f \u062a\u0637\u0628\u064a\u0642 \u0622\u062e\u0631 \u0644\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u0641\u064a \u062a\u0643\u0627\u0645\u0644 \u0627\u0644\u062f\u0648\u0627\u0644 \u0645\u0639 \u0623\u0643\u062b\u0631 \u0645\u0646 \u0645\u062a\u063a\u064a\u0631\u060c \u0623\u064a \u0641\u064a \u0627\u0644\u062a\u0643\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u062b\u0646\u0627\u0626\u064a\u0629 \u0648\u0627\u0644\u062b\u0644\u0627\u062b\u064a\u0629 \u0648\u063a\u064a\u0631\u0647\u0627. \u062d\u064a\u062b \u0623\u0646 \u0645\u062d\u062f\u062f \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u064a\u0633\u0645\u062d <span style=\"color:#1976d2;\"><strong>\u0628\u062a\u063a\u064a\u064a\u0631 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0641\u064a \u0627\u0644\u062a\u0643\u0627\u0645\u0644\u0627\u062a \u0627\u0644\u0645\u062a\u0639\u062f\u062f\u0629<\/strong><\/span> \u062d\u0633\u0628 \u0627\u0644\u0635\u064a\u063a\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-32b139ab326a616a77e4b30bd6123cea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle x=T(x^*)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fc466e0a77ffd809702bfbff6981115d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\int_\\Omega  f(x)dx=\\int_{\\Omega^*} f\\bigl(T(x^*)\\bigr)\\cdot \\begin{vmatrix} \\text{det}\\bigl(JT(x^*)\\bigr)\\end{vmatrix} dx^*\" title=\"Rendered by QuickLaTeX.com\" height=\"40\" width=\"352\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u062d\u064a\u062b T \u0647\u064a \u062f\u0627\u0644\u0629 \u0627\u0644\u062a\u063a\u064a\u064a\u0631 \u0627\u0644\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u062a\u064a \u062a\u0631\u0628\u0637 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0623\u0635\u0644\u064a\u0629 \u0628\u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u062c\u062f\u064a\u062f\u0629.<\/p>\n<p style=\";text-align:right;direction:rtl\"> \u0648\u0623\u062e\u064a\u0631\u064b\u0627\u060c \u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u0635\u0641\u0648\u0641\u0629 \u062c\u0627\u0643\u0648\u0628\u064a \u0623\u064a\u0636\u064b\u0627 \u0644\u0625\u062c\u0631\u0627\u0621 <span style=\"color:#1976d2;\"><strong>\u062a\u0642\u0631\u064a\u0628 \u062e\u0637\u064a<\/strong><\/span> \u0644\u0623\u064a \u062f\u0627\u0644\u0629<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c09a708375fde2676da319bcdfe8b24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"f\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u062d\u0648\u0644 \u0646\u0642\u0637\u0629<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3bf85f1087e9fbed3a319341134ac1a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"p\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: -4px;\"><\/p>\n<p> :<\/p>\n<p style=\";text-align:right;direction:rtl\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-65ba36b611b690e470a1f4c464200fbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle f(x) \\approx f(p) + J_f(p)(x-p)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"208\" style=\"vertical-align: -6px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0633\u062a\u062c\u062f \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u0635\u0641\u062d\u0629 \u0645\u0627 \u0647\u064a \u0645\u0635\u0641\u0648\u0641\u0629 \u062c\u0627\u0643\u0648\u0628\u064a \u0648\u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628\u0647\u0627 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0645\u062b\u0627\u0644. \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0644\u062f\u064a\u0643 \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062a\u064a \u062a\u0645 \u062d\u0644\u0647\u0627 \u0639\u0644\u0649 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0627\u062a \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629 \u062d\u062a\u0649 \u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u0627\u0644\u062a\u062f\u0631\u0628 \u0639\u0644\u064a\u0647\u0627. \u0633\u062a\u0631\u0649 \u0623\u064a\u0636\u064b\u0627 \u0633\u0628\u0628 \u0623\u0647\u0645\u064a\u0629 \u0645\u062d\u062f\u062f \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629\u060c \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629. \u0648\u0623\u062e\u064a\u0631\u0627\u060c \u0646\u0648\u0636\u062d \u0627\u0644\u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u062a\u064a \u062a\u0642\u064a\u0645\u0647\u0627 \u0647\u0630\u0647 \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0645\u0639 \u0627\u0644\u0639\u0645\u0644\u064a\u0627\u062a \u0627\u0644\u0623\u062e\u0631\u0649 \u0648\u0627\u0644\u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0627\u0644\u062a\u064a \u0644\u0647\u0627. \u0645\u0627 \u0647\u064a \u0627\u0644\u0645\u0635\u0641\u0648\u0641\u0629 \u0627\u0644\u064a\u0639\u0642\u0648\u0628\u064a\u0629\u061f 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