{"id":331,"date":"2023-07-06T06:56:27","date_gmt":"2023-07-06T06:56:27","guid":{"rendered":"https:\/\/mathority.org\/ru\/%d1%8f%d0%ba%d0%be%d0%b1%d0%b8%d0%b0%d0%bd%d1%81%d0%ba%d0%b0%d1%8f-%d0%bc%d0%b0%d1%82%d1%80%d0%b8%d1%86%d0%b0\/"},"modified":"2023-07-06T06:56:27","modified_gmt":"2023-07-06T06:56:27","slug":"%d1%8f%d0%ba%d0%be%d0%b1%d0%b8%d0%b0%d0%bd%d1%81%d0%ba%d0%b0%d1%8f-%d0%bc%d0%b0%d1%82%d1%80%d0%b8%d1%86%d0%b0","status":"publish","type":"post","link":"https:\/\/mathority.org\/ru\/%d1%8f%d0%ba%d0%be%d0%b1%d0%b8%d0%b0%d0%bd%d1%81%d0%ba%d0%b0%d1%8f-%d0%bc%d0%b0%d1%82%d1%80%d0%b8%d1%86%d0%b0\/","title":{"rendered":"\u042f\u043a\u043e\u0431\u0438\u0430\u043d \u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u044f\u043a\u043e\u0431\u0438\u0430\u043d\u0430"},"content":{"rendered":"<p>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0438 \u043a\u0430\u043a \u0435\u0435 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0443 \u0432\u0430\u0441 \u0435\u0441\u0442\u044c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u0441 \u043c\u0430\u0442\u0440\u0438\u0446\u0430\u043c\u0438 \u042f\u043a\u043e\u0431\u0438, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u043c\u043e\u0433\u043b\u0438 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f. \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u043f\u043e\u0439\u043c\u0435\u0442\u0435, \u043f\u043e\u0447\u0435\u043c\u0443 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430, \u044f\u043a\u043e\u0431\u0438\u0430\u043d, \u0442\u0430\u043a \u0432\u0430\u0436\u0435\u043d. \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u043c \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u044d\u0442\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u043f\u043e\u0434\u0434\u0435\u0440\u0436\u0438\u0432\u0430\u0435\u0442 \u0441 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u044f\u043c\u0438 \u0438 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f\u043c\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043e\u043d\u0430 \u0438\u043c\u0435\u0435\u0442.<\/p>\n<h2 class=\"wp-block-heading\"> \u0427\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430?<\/h2>\n<p> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0435\u043d\u0438\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0435:<\/p>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"> <strong>\u041c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430<\/strong> \u2014 \u044d\u0442\u043e \u043c\u0430\u0442\u0440\u0438\u0446\u0430, \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u043d\u0430\u044f \u0447\u0430\u0441\u0442\u043d\u044b\u043c\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u043c\u0438 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<p> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u0444\u043e\u0440\u043c\u0443\u043b\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0432\u044b\u0433\u043b\u044f\u0434\u0438\u0442 \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c: <\/p>\n<div class=\"wp-block-image\">\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=\"\u0424\u043e\u0440\u043c\u0443\u043b\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430\" class=\"wp-image-2796\" width=\"477\" height=\"397\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u0421\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438 \u0432\u0441\u0435\u0433\u0434\u0430 \u0431\u0443\u0434\u0443\u0442 \u0438\u043c\u0435\u0442\u044c \u0441\u0442\u043e\u043b\u044c\u043a\u043e \u0436\u0435 \u0441\u0442\u0440\u043e\u043a, \u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<\/p>\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> \u0435\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044f, \u0430 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0441\u0442\u043e\u043b\u0431\u0446\u043e\u0432 \u0431\u0443\u0434\u0435\u0442 \u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u043e\u0432\u0430\u0442\u044c \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u0443 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445<\/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> \u0421 \u0434\u0440\u0443\u0433\u043e\u0439 \u0441\u0442\u043e\u0440\u043e\u043d\u044b, \u044d\u0442\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0442\u0430\u043a\u0436\u0435 \u0438\u0437\u0432\u0435\u0441\u0442\u043d\u0430 \u043a\u0430\u043a <em>\u0434\u0438\u0444\u0444\u0435\u0440\u0435\u043d\u0446\u0438\u0430\u043b\u044c\u043d\u0430\u044f \u043a\u0430\u0440\u0442\u0430 \u042f\u043a\u043e\u0431\u0438<\/em> \u0438\u043b\u0438 <em>\u043b\u0438\u043d\u0435\u0439\u043d\u0430\u044f \u043a\u0430\u0440\u0442\u0430 \u042f\u043a\u043e\u0431\u0438<\/em> . \u041d\u0430 \u0441\u0430\u043c\u043e\u043c \u0434\u0435\u043b\u0435 \u0438\u043d\u043e\u0433\u0434\u0430 \u0435\u0433\u043e \u0442\u043e\u0436\u0435 \u043f\u0438\u0448\u0443\u0442 \u0431\u0443\u043a\u0432\u043e\u0439 D \u0432\u043c\u0435\u0441\u0442\u043e \u0431\u0443\u043a\u0432\u044b J:<\/p>\n<\/p>\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> \u041b\u044e\u0431\u043e\u043f\u044b\u0442\u043d\u043e, \u0447\u0442\u043e \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u043d\u0430\u0437\u0432\u0430\u043d\u0430 \u0432 \u0447\u0435\u0441\u0442\u044c \u041a\u0430\u0440\u043b\u0430 \u0413\u0443\u0441\u0442\u0430\u0432\u0430 \u042f\u043a\u043e\u0431\u0438, \u0432\u044b\u0434\u0430\u044e\u0449\u0435\u0433\u043e\u0441\u044f \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0430 \u0438 \u043f\u0440\u043e\u0444\u0435\u0441\u0441\u043e\u0440\u0430 XIX \u0432\u0435\u043a\u0430, \u0432\u043d\u0435\u0441\u0448\u0435\u0433\u043e \u0432\u0430\u0436\u043d\u044b\u0439 \u0432\u043a\u043b\u0430\u0434 \u0432 \u043c\u0438\u0440 \u043c\u0430\u0442\u0435\u043c\u0430\u0442\u0438\u043a\u0438, \u043e\u0441\u043e\u0431\u0435\u043d\u043d\u043e \u0432 \u043e\u0431\u043b\u0430\u0441\u0442\u044c \u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0439 \u0430\u043b\u0433\u0435\u0431\u0440\u044b.<\/p>\n<h2 class=\"wp-block-heading\"> \u041f\u0440\u0438\u043c\u0435\u0440 \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430<\/h2>\n<p> \u041a\u0430\u043a \u0442\u043e\u043b\u044c\u043a\u043e \u043c\u044b \u043f\u043e\u0437\u043d\u0430\u043a\u043e\u043c\u0438\u043c\u0441\u044f \u0441 \u043f\u043e\u043d\u044f\u0442\u0438\u0435\u043c \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430, \u043c\u044b \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c \u0443\u0432\u0438\u0434\u0438\u043c, \u043a\u0430\u043a \u043e\u043d\u0430 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u044b\u0432\u0430\u0435\u0442\u0441\u044f, \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435:<\/p>\n<ul>\n<li> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u043c \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0432 \u0442\u043e\u0447\u043a\u0435 (1,2) \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/li>\n<\/ul>\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> \u041f\u0435\u0440\u0432\u043e\u0435, \u0447\u0442\u043e \u043d\u0430\u043c \u043d\u0443\u0436\u043d\u043e \u0441\u0434\u0435\u043b\u0430\u0442\u044c, \u044d\u0442\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0432\u0441\u0435 \u0447\u0430\u0441\u0442\u043d\u044b\u0435 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u0435 \u043f\u0435\u0440\u0432\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438: <\/p>\n<\/p>\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 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 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 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> \u0422\u0435\u043f\u0435\u0440\u044c \u043f\u0440\u0438\u043c\u0435\u043d\u0438\u043c \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430. \u0412 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u0434\u0432\u0435 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435 \u0438 \u0434\u0432\u0435 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0431\u0443\u0434\u0435\u0442 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439 \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u0438 2\u00d72: <\/p>\n<div class=\"wp-block-image\">\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> \u041f\u043e\u043b\u0443\u0447\u0438\u0432 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0434\u043b\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430, \u043c\u044b \u043e\u0446\u0435\u043d\u0438\u0432\u0430\u0435\u043c \u0435\u0433\u043e \u0432 \u0442\u043e\u0447\u043a\u0435 (1,2):<\/p>\n<\/p>\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> \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u043f\u0440\u043e\u0432\u043e\u0434\u0438\u043c \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0440\u0435\u0448\u0435\u043d\u0438\u0435: <\/p>\n<div class=\"wp-block-image\">\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=\"\u043f\u0440\u0438\u043c\u0435\u0440 \u0440\u0430\u0441\u0447\u0435\u0442\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430\" class=\"wp-image-2823\" width=\"209\" height=\"71\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> \u041f\u043e\u0441\u043b\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u0432\u044b \u0443\u0437\u043d\u0430\u043b\u0438, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043c\u044b \u043e\u0441\u0442\u0430\u0432\u0438\u043c \u0432\u0430\u043c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439, \u0440\u0435\u0448\u0430\u0435\u043c\u044b\u0445 \u0448\u0430\u0433 \u0437\u0430 \u0448\u0430\u0433\u043e\u043c, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u043c\u043e\u0433\u043b\u0438 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f.<\/p>\n<h2 class=\"wp-block-heading\"> \u0420\u0435\u0448\u0435\u043d\u043d\u044b\u0435 \u043f\u0440\u043e\u0431\u043b\u0435\u043c\u044b \u043c\u0430\u0442\u0440\u0438\u0446 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430<\/h2>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 1<\/h3>\n<p> \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0432 \u0442\u043e\u0447\u043a\u0435 (0,-2) \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0432\u0435\u043a\u0442\u043e\u0440-\u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043e\u0442 2 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445: <\/p>\n<\/p>\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\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0424\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u0434\u0432\u0435 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435 \u0438 \u0434\u0432\u0435 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0431\u0443\u0434\u0435\u0442 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439 \u0440\u0430\u0437\u043c\u0435\u0440\u0430 2\u00d72: <\/p>\n<div class=\"wp-block-image\">\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=\"\u0440\u0435\u0448\u0435\u043d\u043e \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 \u043f\u043e \u043c\u0430\u0442\u0440\u0438\u0446\u0435 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430\" class=\"wp-image-2840\" width=\"511\" height=\"124\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u041f\u043e\u0441\u043b\u0435 \u0442\u043e\u0433\u043e \u043a\u0430\u043a \u043c\u044b \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043b\u0438 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0434\u043b\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430, \u043c\u044b \u043e\u0446\u0435\u043d\u0438\u0432\u0430\u0435\u043c \u0435\u0433\u043e \u0432 \u0442\u043e\u0447\u043a\u0435 (0,-2):<\/p>\n<\/p>\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\"> \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u043f\u0440\u043e\u0432\u043e\u0434\u0438\u043c \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442: <\/p>\n<\/p>\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\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 2<\/h3>\n<p> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0432 \u0442\u043e\u0447\u043a\u0435 (2,-1) \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441 \u0434\u0432\u0443\u043c\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438: <\/p>\n<\/p>\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\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0412 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u0434\u0432\u0435 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435 \u0438 \u0434\u0432\u0435 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u044d\u0442\u043e\u043c\u0443 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0431\u0443\u0434\u0435\u0442 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439 \u0432\u0442\u043e\u0440\u043e\u0433\u043e \u043f\u043e\u0440\u044f\u0434\u043a\u0430:<\/p>\n<\/p>\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\"> \u041d\u0430\u0439\u0434\u044f \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0434\u043b\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430, \u043c\u044b \u043e\u0446\u0435\u043d\u0438\u0432\u0430\u0435\u043c \u0435\u0433\u043e \u0432 \u0442\u043e\u0447\u043a\u0435 (2,-1):<\/p>\n<\/p>\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\"> \u0418, \u043d\u0430\u043a\u043e\u043d\u0435\u0446, \u043f\u0440\u043e\u0432\u043e\u0434\u0438\u043c \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438 \u0438 \u043f\u043e\u043b\u0443\u0447\u0430\u0435\u043c \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442: <\/p>\n<\/p>\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\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 3<\/h3>\n<p> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0432 \u0442\u043e\u0447\u043a\u0435 (2,-2,2) \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441 3 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438: <\/p>\n<\/p>\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\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0412 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u0442\u0440\u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435 \u0438 \u0434\u0432\u0435 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0431\u0443\u0434\u0435\u0442 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u043e\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439 \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u0438 2\u00d73: <\/p>\n<\/p>\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\">\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=\"\u041c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438, \u0440\u0435\u0448\u0430\u044e\u0449\u0435\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 \u0441 3 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438\" class=\"wp-image-2870\" width=\"798\" height=\"121\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u041f\u043e\u043b\u0443\u0447\u0438\u0432 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0434\u043b\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430, \u043c\u044b \u043e\u0446\u0435\u043d\u0438\u0432\u0430\u0435\u043c \u0435\u0433\u043e \u0432 \u0442\u043e\u0447\u043a\u0435 (2,-2,2):<\/p>\n<\/p>\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\"> \u041f\u0440\u043e\u0432\u043e\u0434\u0438\u043c \u0440\u0430\u0441\u0447\u0435\u0442\u044b:<\/p>\n<\/p>\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\"> \u0418 \u043f\u0440\u043e\u0434\u043e\u043b\u0436\u0430\u0435\u043c \u0434\u0435\u0439\u0441\u0442\u0432\u043e\u0432\u0430\u0442\u044c \u0434\u043e \u0442\u0435\u0445 \u043f\u043e\u0440, \u043f\u043e\u043a\u0430 \u0435\u0433\u043e \u0443\u0436\u0435 \u043d\u0435\u043b\u044c\u0437\u044f \u0431\u0443\u0434\u0435\u0442 \u0443\u043f\u0440\u043e\u0441\u0442\u0438\u0442\u044c: <\/p>\n<\/p>\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\"><\/div>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<h3 class=\"wp-block-heading\"> \u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 4<\/h3>\n<p> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0432 \u0442\u043e\u0447\u043a\u0435<strong> <\/strong><\/p>\n<\/p>\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>\u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u043c\u043d\u043e\u0433\u0438\u0445 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445: <\/p>\n<\/p>\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\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0412 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u0434\u0432\u0435 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435 \u0438 \u0442\u0440\u0438 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0431\u0443\u0434\u0435\u0442 \u043f\u0440\u044f\u043c\u043e\u0443\u0433\u043e\u043b\u044c\u043d\u043e\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439 \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u0438 3\u00d72: <\/p>\n<div class=\"wp-block-image\">\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=\"\u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 \u043f\u043e\u0448\u0430\u0433\u043e\u0432\u043e \u0440\u0435\u0448\u0430\u0435\u0442 \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430\" class=\"wp-image-2886\" width=\"704\" height=\"192\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u041f\u043e\u043b\u0443\u0447\u0438\u0432 \u0432\u044b\u0440\u0430\u0436\u0435\u043d\u0438\u0435 \u0434\u043b\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430, \u043c\u044b \u043e\u0446\u0435\u043d\u0438\u0432\u0430\u0435\u043c \u0435\u0433\u043e \u0434\u043e \u0442\u043e\u0447\u043a\u0438 <\/p>\n<\/p>\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 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\"> \u041c\u044b \u0432\u044b\u043f\u043e\u043b\u043d\u044f\u0435\u043c \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438:<\/p>\n<\/p>\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\"> \u0422\u0430\u043a\u0438\u043c \u043e\u0431\u0440\u0430\u0437\u043e\u043c, \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438 \u0432\u0435\u043a\u0442\u043e\u0440\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0432 \u0440\u0430\u0441\u0441\u043c\u0430\u0442\u0440\u0438\u0432\u0430\u0435\u043c\u043e\u0439 \u0442\u043e\u0447\u043a\u0435 \u0438\u043c\u0435\u0435\u0442 \u0432\u0438\u0434: <\/p>\n<\/p>\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\"><\/div>\n<h3 class=\"wp-block-heading\">\u0423\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0435 5<\/h3>\n<p> \u0412\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0432 \u0442\u043e\u0447\u043a\u0435<\/p>\n<\/p>\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> \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441 \u0442\u0440\u0435\u043c\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438: <\/p>\n<\/p>\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\">\n<div class=\"otfm-sp__title\"> <strong>\u043f\u043e\u0441\u043c\u043e\u0442\u0440\u0435\u0442\u044c \u0440\u0435\u0448\u0435\u043d\u0438\u0435<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> \u0412 \u0434\u0430\u043d\u043d\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u0442\u0440\u0438 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445 \u0438 \u0442\u0440\u0438 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0431\u0443\u0434\u0435\u0442 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043d\u043e\u0439 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439 \u0440\u0430\u0437\u043c\u0435\u0440\u043d\u043e\u0441\u0442\u0438 3\u00d73: <\/p>\n<\/p>\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\">\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=\"\u0420\u0435\u0448\u0435\u043d\u0438\u0435 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u044f \u0441 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 3x3 \u0441 3 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438\" class=\"wp-image-2937\" width=\"629\" height=\"191\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-left\"> \u041d\u0430\u0439\u0434\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430, \u043c\u044b \u043e\u0446\u0435\u043d\u0438\u0432\u0430\u0435\u043c \u0435\u0435 \u0432 \u0442\u043e\u0447\u043a\u0435 <\/p>\n<\/p>\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 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\"> \u0420\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0435\u043c \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u0438:<\/p>\n<\/p>\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\"> \u0418 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435: <\/p>\n<\/p>\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\"><\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-118\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430: \u044f\u043a\u043e\u0431\u0438\u0430\u043d<\/h2>\n<p> \u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u043d\u0430\u0437\u044b\u0432\u0430\u0435\u0442\u0441\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u0435\u043c <strong>\u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430<\/strong> \u0438\u043b\u0438 \u044f\u043a\u043e\u0431\u0438\u0430\u043d\u043e\u043c. \u041d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0443\u0447\u0438\u0442\u044b\u0432\u0430\u0442\u044c, \u0447\u0442\u043e \u044f\u043a\u043e\u0431\u0438\u0430\u043d \u043c\u043e\u0436\u043d\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u0442\u043e\u043b\u044c\u043a\u043e \u0432 \u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435, \u0435\u0441\u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u0442\u0430\u043a\u043e\u0435 \u0436\u0435 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445, \u043a\u0430\u043a \u0438 \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u044b\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u0442\u043e\u0433\u0434\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0431\u0443\u0434\u0435\u0442 \u0438\u043c\u0435\u0442\u044c \u0442\u0430\u043a\u043e\u0435 \u0436\u0435 \u043a\u043e\u043b\u0438\u0447\u0435\u0441\u0442\u0432\u043e \u0441\u0442\u0440\u043e\u043a, \u043a\u0430\u043a \u0438 \u0441\u0442\u043e\u043b\u0431\u0446\u043e\u0432, \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043e\u043d\u0430 \u0431\u0443\u0434\u0435\u0442 \u043a\u0432\u0430\u0434\u0440\u0430\u0442\u043e\u043c. \u043c\u0430\u0442\u0440\u0438\u0446\u0430. .<\/p>\n<h3 class=\"wp-block-heading\"> \u043f\u0440\u0438\u043c\u0435\u0440 \u044f\u043a\u043e\u0431\u0438\u0430\u043d\u0430<\/h3>\n<p> \u0420\u0430\u0441\u0441\u043c\u043e\u0442\u0440\u0438\u043c \u043f\u0440\u0438\u043c\u0435\u0440 \u0432\u044b\u0447\u0438\u0441\u043b\u0435\u043d\u0438\u044f \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044f \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0441 \u0434\u0432\u0443\u043c\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u043c\u0438:<\/p>\n<\/p>\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> \u0421\u043d\u0430\u0447\u0430\u043b\u0430 \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u043c \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u042f\u043a\u043e\u0431\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/p>\n<\/p>\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\"> \u0410 \u0442\u0435\u043f\u0435\u0440\u044c \u0440\u0435\u0448\u0430\u0435\u043c \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b 2\u04452:<\/p>\n<\/p>\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\"> \u042f\u043a\u043e\u0431\u0438\u0430\u043d \u0438 \u043e\u0431\u0440\u0430\u0442\u0438\u043c\u043e\u0441\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/h2>\n<p> \u0422\u0435\u043f\u0435\u0440\u044c, \u043a\u043e\u0433\u0434\u0430 \u0432\u044b \u043f\u043e\u0437\u043d\u0430\u043a\u043e\u043c\u0438\u043b\u0438\u0441\u044c \u0441 \u043a\u043e\u043d\u0446\u0435\u043f\u0446\u0438\u0435\u0439 \u044f\u043a\u043e\u0431\u0438\u0430\u043d\u0430, \u0432\u044b, \u0432\u0435\u0440\u043e\u044f\u0442\u043d\u043e, \u043f\u043e\u0434\u0443\u043c\u0430\u043b\u0438\u2026 \u043d\u0443 \u043a\u0430\u043a\u043e\u0439 \u0432 \u044d\u0442\u043e\u043c \u0441\u043c\u044b\u0441\u043b?<\/p>\n<p> \u0418\u0442\u0430\u043a, \u043e\u0441\u043d\u043e\u0432\u043d\u043e\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u044f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u2014 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u044c, \u043c\u043e\u0436\u043d\u043e \u043b\u0438 \u043e\u0431\u0440\u0430\u0442\u0438\u0442\u044c \u0444\u0443\u043d\u043a\u0446\u0438\u044e. <strong>\u0422\u0435\u043e\u0440\u0435\u043c\u0430 \u043e\u0431 \u043e\u0431\u0440\u0430\u0442\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438<\/strong> \u0433\u043b\u0430\u0441\u0438\u0442, \u0447\u0442\u043e \u0435\u0441\u043b\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 (\u044f\u043a\u043e\u0431\u0438\u0430\u043d) \u043e\u0442\u043b\u0438\u0447\u0435\u043d \u043e\u0442 0, \u044d\u0442\u043e \u043e\u0437\u043d\u0430\u0447\u0430\u0435\u0442, \u0447\u0442\u043e \u044d\u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u0431\u0440\u0430\u0442\u0438\u043c\u0430.<\/p>\n<\/p>\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> \u0421\u043b\u0435\u0434\u0443\u0435\u0442 \u043e\u0442\u043c\u0435\u0442\u0438\u0442\u044c, \u0447\u0442\u043e \u044d\u0442\u043e \u0443\u0441\u043b\u043e\u0432\u0438\u0435 \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u044b\u043c, \u043d\u043e \u043d\u0435\u0434\u043e\u0441\u0442\u0430\u0442\u043e\u0447\u043d\u044b\u043c, \u0442\u043e \u0435\u0441\u0442\u044c, \u0435\u0441\u043b\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043d\u0435\u043d\u0443\u043b\u0435\u0432\u043e\u0439, \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0443\u0442\u0432\u0435\u0440\u0436\u0434\u0430\u0442\u044c, \u0447\u0442\u043e \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u043c\u043e\u0436\u043d\u043e \u0438\u043d\u0432\u0435\u0440\u0442\u0438\u0440\u043e\u0432\u0430\u0442\u044c, \u043e\u0434\u043d\u0430\u043a\u043e, \u0435\u0441\u043b\u0438 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u0440\u0430\u0432\u0435\u043d 0, \u043c\u044b \u043d\u0435 \u043c\u043e\u0436\u0435\u043c \u0437\u043d\u0430\u0442\u044c, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u043c\u0435\u0435\u0442 \u043e\u0431\u0440\u0430\u0442\u043d\u0443\u044e \u0438\u043b\u0438 \u043d\u0435\u0442.<\/p>\n<p> \u041d\u0430\u043f\u0440\u0438\u043c\u0435\u0440, \u0432 \u043f\u0440\u0438\u0432\u0435\u0434\u0435\u043d\u043d\u043e\u043c \u0440\u0430\u043d\u0435\u0435 \u043f\u0440\u0438\u043c\u0435\u0440\u0435 \u0442\u043e\u0433\u043e, \u043a\u0430\u043a \u043d\u0430\u0439\u0442\u0438 \u044f\u043a\u043e\u0431\u0438\u0430\u043d \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u0434\u0430\u0435\u0442<\/p>\n<\/p>\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> . \u0412 \u044d\u0442\u043e\u043c \u0441\u043b\u0443\u0447\u0430\u0435 \u043c\u044b \u043c\u043e\u0436\u0435\u043c \u0443\u0442\u0432\u0435\u0440\u0436\u0434\u0430\u0442\u044c, \u0447\u0442\u043e \u0444\u0443\u043d\u043a\u0446\u0438\u044e \u043c\u043e\u0436\u043d\u043e \u043e\u0431\u0440\u0430\u0442\u0438\u0442\u044c \u0432\u0441\u0435\u0433\u0434\u0430, \u043a\u0440\u043e\u043c\u0435 \u0442\u043e\u0447\u043a\u0438 (0,0), \u0442\u0430\u043a \u043a\u0430\u043a \u044d\u0442\u0430 \u0442\u043e\u0447\u043a\u0430 \u2014 \u0435\u0434\u0438\u043d\u0441\u0442\u0432\u0435\u043d\u043d\u0430\u044f, \u0433\u0434\u0435 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u042f\u043a\u043e\u0431\u0438 \u0440\u0430\u0432\u0435\u043d \u043d\u0443\u043b\u044e \u0438, \u0441\u043b\u0435\u0434\u043e\u0432\u0430\u0442\u0435\u043b\u044c\u043d\u043e, \u043c\u044b \u043d\u0435 \u0437\u043d\u0430\u0435\u043c, \u0431\u0443\u0434\u0435\u0442 \u043b\u0438 \u043e\u0431\u0440\u0430\u0442\u043d\u0430\u044f \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0441\u0443\u0449\u0435\u0441\u0442\u0432\u0443\u0435\u0442 \u0432 \u044d\u0442\u043e\u0439 \u0442\u043e\u0447\u043a\u0435. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-119\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"> \u0421\u0432\u044f\u0437\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438 \u0441 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u044f\u043c\u0438<\/h2>\n<p> \u041c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0441\u0432\u044f\u0437\u0430\u043d\u0430 \u0441 \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u043e\u043c \u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439 \u0413\u0435\u0441\u0441\u0435 \u0444\u0443\u043d\u043a\u0446\u0438\u0438:<\/p>\n<h3 class=\"wp-block-heading\"> \u0421\u043a\u043b\u043e\u043d<\/h3>\n<p> \u0415\u0441\u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u0441\u043a\u0430\u043b\u044f\u0440\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0435\u0439, \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0431\u0443\u0434\u0435\u0442 \u043c\u0430\u0442\u0440\u0438\u0446\u0435\u0439-\u0441\u0442\u0440\u043e\u043a\u043e\u0439, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0431\u0443\u0434\u0435\u0442 \u044d\u043a\u0432\u0438\u0432\u0430\u043b\u0435\u043d\u0442\u043d\u0430 <strong>\u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u0443<\/strong> : <\/p>\n<\/p>\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 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\"> \u041c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435<\/h3>\n<p> \u041c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438 \u0433\u0440\u0430\u0434\u0438\u0435\u043d\u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0438 \u0440\u0430\u0432\u043d\u0430 <strong>\u043c\u0430\u0442\u0440\u0438\u0446\u0435 \u0413\u0435\u0441\u0441\u0438\u0430\u043d\u0430<\/strong> :<\/p>\n<\/p>\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> \u0413\u0435\u0441\u0441\u0438\u0430\u043d \u2014 \u043e\u0447\u0435\u043d\u044c \u0432\u0430\u0436\u043d\u0430\u044f \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0434\u043b\u044f \u0432\u044b\u0432\u043e\u0434\u0430 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0441 \u0431\u043e\u043b\u0435\u0435 \u0447\u0435\u043c \u043e\u0434\u043d\u043e\u0439 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439, \u043f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043e\u043d\u0430 \u0444\u043e\u0440\u043c\u0438\u0440\u0443\u0435\u0442\u0441\u044f \u0432\u0442\u043e\u0440\u044b\u043c\u0438 \u043f\u0440\u043e\u0438\u0437\u0432\u043e\u0434\u043d\u044b\u043c\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438. \u0424\u0430\u043a\u0442\u0438\u0447\u0435\u0441\u043a\u0438, \u043c\u043e\u0436\u043d\u043e \u0441\u043a\u0430\u0437\u0430\u0442\u044c, \u0447\u0442\u043e  \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0413\u0435\u0441\u0441\u0435  \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043d\u0435\u043f\u0440\u0435\u0440\u044b\u0432\u043d\u043e\u0441\u0442\u044c\u044e \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430. \u041d\u043e \u044d\u0442\u043e \u043d\u0430\u0441\u0442\u043e\u043b\u044c\u043a\u043e \u0432\u0430\u0436\u043d\u043e, \u0447\u0442\u043e \u0443 \u043d\u0430\u0441 \u0435\u0441\u0442\u044c \u0446\u0435\u043b\u0430\u044f \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0430, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u043f\u043e\u0434\u0440\u043e\u0431\u043d\u043e \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u0442 \u044d\u0442\u043e. \u0422\u0430\u043a \u0447\u0442\u043e \u0435\u0441\u043b\u0438 \u0432\u044b \u0445\u043e\u0442\u0438\u0442\u0435 \u0442\u043e\u0447\u043d\u043e \u0443\u0437\u043d\u0430\u0442\u044c, \u0447\u0442\u043e \u044d\u0442\u043e \u0437\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u0438 \u043f\u043e\u0447\u0435\u043c\u0443 \u043e\u043d\u0430 \u0442\u0430\u043a\u0430\u044f \u043e\u0441\u043e\u0431\u0435\u043d\u043d\u0430\u044f, \u0432\u044b \u043c\u043e\u0436\u0435\u0442\u0435 \u043f\u0435\u0440\u0435\u0439\u0442\u0438 \u043f\u043e \u0441\u0441\u044b\u043b\u043a\u0435.<\/p>\n<h2 class=\"wp-block-heading\"> \u041f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430<\/h2>\n<div class=\"adsb30\" style=\" margin:px; text-align:\"><\/div>\n<p> \u041f\u043e\u043c\u0438\u043c\u043e \u0437\u0430\u043c\u0435\u0447\u0435\u043d\u043d\u043e\u0439 \u043d\u0430\u043c\u0438 \u043f\u043e\u043b\u0435\u0437\u043d\u043e\u0441\u0442\u0438 \u044f\u043a\u043e\u0431\u0438\u0430\u043d\u0430, \u043a\u043e\u0442\u043e\u0440\u044b\u0439 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u044f\u0435\u0442, \u044f\u0432\u043b\u044f\u0435\u0442\u0441\u044f \u043b\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u043e\u0431\u0440\u0430\u0442\u0438\u043c\u043e\u0439, \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0438\u043c\u0435\u0435\u0442 \u0438 \u0434\u0440\u0443\u0433\u0438\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u044f.<\/p>\n<p> \u041c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f \u0440\u0430\u0441\u0447\u0435\u0442\u0430 <strong><span style=\"color:#1976d2;\">\u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0445 \u0442\u043e\u0447\u0435\u043a<\/span><\/strong> \u043c\u043d\u043e\u0433\u043e\u043c\u0435\u0440\u043d\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u0437\u0430\u0442\u0435\u043c \u043a\u043b\u0430\u0441\u0441\u0438\u0444\u0438\u0446\u0438\u0440\u0443\u044e\u0442\u0441\u044f \u043d\u0430 \u043c\u0430\u043a\u0441\u0438\u043c\u0443\u043c\u044b, \u043c\u0438\u043d\u0438\u043c\u0443\u043c\u044b \u0438\u043b\u0438 \u0441\u0435\u0434\u043b\u043e\u0432\u044b\u0435 \u0442\u043e\u0447\u043a\u0438 \u0441 \u043f\u043e\u043c\u043e\u0449\u044c\u044e \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u0413\u0435\u0441\u0441\u0435. \u0427\u0442\u043e\u0431\u044b \u043d\u0430\u0439\u0442\u0438 \u043a\u0440\u0438\u0442\u0438\u0447\u0435\u0441\u043a\u0438\u0435 \u0442\u043e\u0447\u043a\u0438, \u043d\u0435\u043e\u0431\u0445\u043e\u0434\u0438\u043c\u043e \u0432\u044b\u0447\u0438\u0441\u043b\u0438\u0442\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u0443 \u042f\u043a\u043e\u0431\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0438, \u043f\u0440\u0438\u0440\u0430\u0432\u043d\u044f\u0442\u044c \u0435\u0435 \u043a 0 \u0438 \u0440\u0435\u0448\u0438\u0442\u044c \u043f\u043e\u043b\u0443\u0447\u0435\u043d\u043d\u044b\u0435 \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u044f.<\/p>\n<\/p>\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> \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0434\u0440\u0443\u0433\u043e\u0435 \u043f\u0440\u0438\u043c\u0435\u043d\u0435\u043d\u0438\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u043d\u0430\u0445\u043e\u0434\u0438\u0442\u0441\u044f \u043f\u0440\u0438 \u0438\u043d\u0442\u0435\u0433\u0440\u0438\u0440\u043e\u0432\u0430\u043d\u0438\u0438 \u0444\u0443\u043d\u043a\u0446\u0438\u0439 \u0441 \u0431\u043e\u043b\u0435\u0435 \u0447\u0435\u043c \u043e\u0434\u043d\u043e\u0439 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439, \u0442. \u0435. \u0432 \u0434\u0432\u043e\u0439\u043d\u044b\u0445, \u0442\u0440\u043e\u0439\u043d\u044b\u0445 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u0430\u0445 \u0438 \u0442. \u0434. \u041f\u043e\u0441\u043a\u043e\u043b\u044c\u043a\u0443 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438 \u0434\u043e\u043f\u0443\u0441\u043a\u0430\u0435\u0442 <span style=\"color:#1976d2;\"><strong>\u0437\u0430\u043c\u0435\u043d\u0443 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u043e\u0439 \u0432 \u043a\u0440\u0430\u0442\u043d\u044b\u0445 \u0438\u043d\u0442\u0435\u0433\u0440\u0430\u043b\u0430\u0445<\/strong><\/span> \u043f\u043e \u0441\u043b\u0435\u0434\u0443\u044e\u0449\u0435\u0439 \u0444\u043e\u0440\u043c\u0443\u043b\u0435:<\/p>\n<\/p>\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 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> \u0413\u0434\u0435 T \u2014 \u0444\u0443\u043d\u043a\u0446\u0438\u044f \u0438\u0437\u043c\u0435\u043d\u0435\u043d\u0438\u044f \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0445, \u043a\u043e\u0442\u043e\u0440\u0430\u044f \u0441\u0432\u044f\u0437\u044b\u0432\u0430\u0435\u0442 \u0438\u0441\u0445\u043e\u0434\u043d\u044b\u0435 \u043f\u0435\u0440\u0435\u043c\u0435\u043d\u043d\u044b\u0435 \u0441 \u043d\u043e\u0432\u044b\u043c\u0438.<\/p>\n<p> \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0442\u0430\u043a\u0436\u0435 \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u0435\u0442\u0441\u044f \u0434\u043b\u044f <span style=\"color:#1976d2;\"><strong>\u043b\u0438\u043d\u0435\u0439\u043d\u043e\u0433\u043e \u043f\u0440\u0438\u0431\u043b\u0438\u0436\u0435\u043d\u0438\u044f<\/strong><\/span> \u043b\u044e\u0431\u043e\u0439 \u0444\u0443\u043d\u043a\u0446\u0438\u0438.<\/p>\n<\/p>\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> \u0432\u043e\u043a\u0440\u0443\u0433 \u0442\u043e\u0447\u043a\u0438<\/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>\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>\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0438 \u043a\u0430\u043a \u0435\u0435 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0443 \u0432\u0430\u0441 \u0435\u0441\u0442\u044c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u0441 \u043c\u0430\u0442\u0440\u0438\u0446\u0430\u043c\u0438 \u042f\u043a\u043e\u0431\u0438, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u043c\u043e\u0433\u043b\u0438 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f. \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u043f\u043e\u0439\u043c\u0435\u0442\u0435, \u043f\u043e\u0447\u0435\u043c\u0443 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430, \u044f\u043a\u043e\u0431\u0438\u0430\u043d, \u0442\u0430\u043a \u0432\u0430\u0436\u0435\u043d. \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u043c \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u044d\u0442\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u043f\u043e\u0434\u0434\u0435\u0440\u0436\u0438\u0432\u0430\u0435\u0442 \u0441 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u044f\u043c\u0438 \u0438 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f\u043c\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043e\u043d\u0430 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/ru\/%d1%8f%d0%ba%d0%be%d0%b1%d0%b8%d0%b0%d0%bd%d1%81%d0%ba%d0%b0%d1%8f-%d0%bc%d0%b0%d1%82%d1%80%d0%b8%d1%86%d0%b0\/\"> <span class=\"screen-reader-text\">\u042f\u043a\u043e\u0431\u0438\u0430\u043d \u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u044f\u043a\u043e\u0431\u0438\u0430\u043d\u0430<\/span> \u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[20],"tags":[],"class_list":["post-331","post","type-post","status-publish","format-standard","hentry","category-20"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u042f\u043a\u043e\u0431\u0438\u0430\u043d \u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 - \u041c\u0430\u0442\u043e\u0440\u043d\u043e\u0441\u0442\u044c<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/ru\/\u044f\u043a\u043e\u0431\u0438\u0430\u043d\u0441\u043a\u0430\u044f-\u043c\u0430\u0442\u0440\u0438\u0446\u0430\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u042f\u043a\u043e\u0431\u0438\u0430\u043d \u0438 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 - \u041c\u0430\u0442\u043e\u0440\u043d\u043e\u0441\u0442\u044c\" \/>\n<meta property=\"og:description\" content=\"\u041d\u0430 \u044d\u0442\u043e\u0439 \u0441\u0442\u0440\u0430\u043d\u0438\u0446\u0435 \u0432\u044b \u0443\u0437\u043d\u0430\u0435\u0442\u0435, \u0447\u0442\u043e \u0442\u0430\u043a\u043e\u0435 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430 \u0438 \u043a\u0430\u043a \u0435\u0435 \u0440\u0430\u0441\u0441\u0447\u0438\u0442\u0430\u0442\u044c \u043d\u0430 \u043f\u0440\u0438\u043c\u0435\u0440\u0435. \u041a\u0440\u043e\u043c\u0435 \u0442\u043e\u0433\u043e, \u0443 \u0432\u0430\u0441 \u0435\u0441\u0442\u044c \u043d\u0435\u0441\u043a\u043e\u043b\u044c\u043a\u043e \u0440\u0435\u0448\u0435\u043d\u043d\u044b\u0445 \u0443\u043f\u0440\u0430\u0436\u043d\u0435\u043d\u0438\u0439 \u0441 \u043c\u0430\u0442\u0440\u0438\u0446\u0430\u043c\u0438 \u042f\u043a\u043e\u0431\u0438, \u0447\u0442\u043e\u0431\u044b \u0432\u044b \u043c\u043e\u0433\u043b\u0438 \u043f\u043e\u043f\u0440\u0430\u043a\u0442\u0438\u043a\u043e\u0432\u0430\u0442\u044c\u0441\u044f. \u0412\u044b \u0442\u0430\u043a\u0436\u0435 \u043f\u043e\u0439\u043c\u0435\u0442\u0435, \u043f\u043e\u0447\u0435\u043c\u0443 \u043e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u0442\u0435\u043b\u044c \u043c\u0430\u0442\u0440\u0438\u0446\u044b \u042f\u043a\u043e\u0431\u0438\u0430\u043d\u0430, \u044f\u043a\u043e\u0431\u0438\u0430\u043d, \u0442\u0430\u043a \u0432\u0430\u0436\u0435\u043d. \u041d\u0430\u043a\u043e\u043d\u0435\u0446, \u043c\u044b \u043e\u0431\u044a\u044f\u0441\u043d\u044f\u0435\u043c \u043e\u0442\u043d\u043e\u0448\u0435\u043d\u0438\u044f, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u044d\u0442\u0430 \u043c\u0430\u0442\u0440\u0438\u0446\u0430 \u043f\u043e\u0434\u0434\u0435\u0440\u0436\u0438\u0432\u0430\u0435\u0442 \u0441 \u0434\u0440\u0443\u0433\u0438\u043c\u0438 \u043e\u043f\u0435\u0440\u0430\u0446\u0438\u044f\u043c\u0438 \u0438 \u043f\u0440\u0438\u043b\u043e\u0436\u0435\u043d\u0438\u044f\u043c\u0438, \u043a\u043e\u0442\u043e\u0440\u044b\u0435 \u043e\u043d\u0430 &hellip; 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