{"id":33394,"date":"2024-11-30T13:00:05","date_gmt":"2024-11-30T13:00:05","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=33394"},"modified":"2025-07-21T04:30:34","modified_gmt":"2025-07-21T04:30:34","slug":"%d9%85%d8%b4%d8%aa%d9%82%d8%a7%d8%aa-%d9%83%d8%ab%d9%8a%d8%b1%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d9%88%d8%a7%d9%84%d8%af%d9%88%d8%a7%d9%84-%d8%a7%d9%84%d9%85%d8%ab%d9%84%d8%ab%d9%8a","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/ar\/%d9%85%d8%b4%d8%aa%d9%82%d8%a7%d8%aa-%d9%83%d8%ab%d9%8a%d8%b1%d8%a7%d8%aa-%d8%a7%d9%84%d8%ad%d8%af%d9%88%d8%af-%d9%88%d8%a7%d9%84%d8%af%d9%88%d8%a7%d9%84-%d8%a7%d9%84%d9%85%d8%ab%d9%84%d8%ab%d9%8a\/","title":{"rendered":"\u0645\u0634\u062a\u0642\u0627\u062a \u0643\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f \u0648\u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 \u0648\u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645"},"content":{"rendered":"<style>\np, ul, ol{\ntext-align: justify;\n}\nh1{\ntext-align:center;\ntext-transform: uppercase;\n}\nh2{\ntext-align:center;\ntext-transform: uppercase;\nfont-size:24pt;\n}\nh3 { \n    text-align: center;\n    text-transform: uppercase;\n    font-size: 24px !important;\n}\n<\/style>\n<style><span data-mce-type=\"bookmark\" style=\"display: inline-block; width: 0px; overflow: hidden; line-height: 0;\" class=\"mce_SELRES_start\"><\/span><br \/>\np, ul, ol{\ntext-align: justify;\n}\nh1{\ntext-align:center;\ntext-transform: uppercase;\n}\nh2{\ntext-align:center;\ntext-transform: uppercase;\nfont-size:24pt;\n}\nh3 { \n    text-align: center;\n    text-transform: uppercase;\n    font-size: 24px !important;\n}\n<\/style>\n<h1>\u0645\u0634\u062a\u0642\u0627\u062a \u0643\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f \u0648\u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 \u0648\u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645<\/h1>\n<p style=\"text-align:center;\"><em><br \/>\n\u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0647\u064a \u0623\u062f\u0627\u0629 \u0645\u062d\u0648\u0631\u064a\u0629 \u0641\u064a \u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u060c \u0648\u0644\u0647\u0627 \u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u0627\u0644\u0639\u0644\u0648\u0645 \u0648\u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0648\u0627\u0644\u0627\u0642\u062a\u0635\u0627\u062f. \u064a\u0642\u062f\u0645 \u0647\u0630\u0627 \u0627\u0644\u0645\u0642\u0627\u0644 \u062f\u0644\u064a\u0644\u0627\u064b \u062a\u062f\u0631\u064a\u062c\u064a\u0627\u064b \u0644\u0625\u062a\u0642\u0627\u0646 \u0627\u0634\u062a\u0642\u0627\u0642 \u0627\u0644\u062f\u0648\u0627\u0644\u060c \u0628\u062f\u0621\u064b\u0627 \u0645\u0646 \u0643\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f \u0648\u062d\u062a\u0649 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 \u0648\u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u064a\u0629. \u0648\u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0648\u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0627\u0644\u0645\u0644\u0645\u0648\u0633\u0629\u060c \u064a\u0633\u0639\u0649 \u0647\u0630\u0627 \u0627\u0644\u0645\u0642\u0627\u0644 \u0625\u0644\u0649 \u062a\u0648\u0636\u064a\u062d \u0643\u064a\u0641\u064a\u0629 \u062a\u0637\u0628\u064a\u0642 \u0642\u0648\u0627\u0639\u062f \u0627\u0644\u0627\u0634\u062a\u0642\u0627\u0642 \u0648\u0641\u0647\u0645 \u0627\u0644\u0623\u0633\u0627\u0633 \u0627\u0644\u0646\u0638\u0631\u064a \u0644\u0647\u0627.<br \/>\n<\/em><\/p>\n<p style=\"text-align:center;\"><strong>\u0623\u0647\u062f\u0627\u0641 \u0627\u0644\u062a\u0639\u0644\u0645<\/strong><\/p>\n<ol>\n<li><strong>\u0641\u0647\u0645<\/strong> \u0627\u0644\u0645\u0641\u0647\u0648\u0645 \u0627\u0644\u0639\u0627\u0645 \u0644\u0644\u0645\u0634\u062a\u0642\u0629 \u0648\u062e\u0635\u0627\u0626\u0635\u0647\u0627 \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629.<\/li>\n<li><strong>\u062a\u0637\u0628\u064a\u0642<\/strong> \u0627\u0644\u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0631\u0633\u0645\u064a \u0644\u0644\u0645\u0634\u062a\u0642\u0629 \u0644\u062d\u0633\u0627\u0628 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629.<\/li>\n<li><strong>\u0625\u062b\u0628\u0627\u062a<\/strong> \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062b\u0627\u0628\u062a\u0629 \u0648\u062f\u0627\u0644\u0629 \u0627\u0644\u0647\u0648\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a.<\/li>\n<li><strong>\u0627\u0633\u062a\u062e\u0644\u0627\u0635<\/strong> \u0642\u0648\u0627\u0639\u062f \u0627\u0634\u062a\u0642\u0627\u0642 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 \u0627\u0646\u0637\u0644\u0627\u0642\u064b\u0627 \u0645\u0646 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0644\u062c\u064a\u0628 \u0648\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645.<\/li>\n<li><strong>\u062d\u0633\u0627\u0628<\/strong> \u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 \u0627\u0644\u0645\u0631\u0643\u0628\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0642\u0648\u0627\u0639\u062f \u0627\u0644\u062c\u0628\u0631\u064a\u0629.<\/li>\n<li><strong>\u0625\u062b\u0628\u0627\u062a<\/strong> \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0628\u0637\u0631\u064a\u0642\u0629 \u0631\u0633\u0645\u064a\u0629 \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0646\u0647\u0627\u064a\u0627\u062a.<\/li>\n<\/ol>\n<p style=\"text-align:center\">\n<strong><u>\u0641\u0647\u0631\u0633 \u0627\u0644\u0645\u062d\u062a\u0648\u064a\u0627\u062a<\/u>:<\/strong><br \/>\n<a href=\"#1\">\u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062c\u0628\u0631\u064a\u0629<\/a><br \/>\n<a href=\"#2\">\u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062a\u0633\u0627\u0645\u064a\u0629<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" title=\"YouTube video player\" data-src=\"https:\/\/www.youtube.com\/embed\/LudVXLRnmLw\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p>\u062d\u062a\u0649 \u0627\u0644\u0622\u0646\u060c \u0642\u0645\u0646\u0627 \u0641\u0642\u0637 \u0628\u0645\u0631\u0627\u062c\u0639\u0629 \u0645\u0627 \u0647\u064a \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0648\u0628\u0639\u0636 \u062e\u0635\u0627\u0626\u0635\u0647\u0627 \u0627\u0644\u062c\u0628\u0631\u064a\u0629\u060c \u0644\u0643\u0646\u0646\u0627 \u0644\u0645 \u0646\u062a\u062d\u062f\u062b \u0639\u0646 \u0643\u064a\u0641\u064a\u0629 \u062d\u0633\u0627\u0628\u0647\u0627. \u0647\u0646\u0627 \u0633\u0646\u0639\u0627\u0644\u062c \u0647\u0630\u0647 \u0627\u0644\u0645\u0633\u0623\u0644\u0629 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0639\u0631\u0636 \u0643\u0644 \u062a\u0642\u0646\u064a\u0629 \u0645\u0646 \u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u0627\u0634\u062a\u0642\u0627\u0642\u060c \u0648\u0643\u064a\u0641\u064a\u0629 \u0627\u0633\u062a\u062e\u0644\u0627\u0635\u0647\u0627 \u0644\u0643\u0644 \u062d\u0627\u0644\u0629.<\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062c\u0628\u0631\u064a\u0629<\/h2>\n<h3>\u0627\u0644\u062f\u0627\u0644\u0629 \u0627\u0644\u062b\u0627\u0628\u062a\u0629<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=LudVXLRnmLw&amp;t=104s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = c,<\/span><\/span> \u062d\u064a\u062b <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">c<\/span><\/span><\/span> <\/strong><\/a>\u0639\u062f\u062f\u064b\u0627 \u062d\u0642\u064a\u0642\u064a\u064b\u0627 \u062b\u0627\u0628\u062a\u064b\u0627\u060c \u0641\u0625\u0646\u0647 \u064a\u0643\u0648\u0646:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{df(x)}{dx} =\\frac{d}{dx}c = 0<\/span><\/span><\/p>\n<p><span style=\"color: #000080;\"><strong>\u0627\u0644\u0628\u0631\u0647\u0627\u0646:<\/strong><\/span> \u0641\u064a \u0627\u0644\u0648\u0627\u0642\u0639\u060c \u0647\u0630\u0627 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u064a\u062a\u0645 \u0641\u064a \u062e\u0637\u0648\u0629 \u0648\u0627\u062d\u062f\u0629 \u0641\u0642\u0637:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rll}\n\n(1) &amp;\\displaystyle \\dfrac{d}{dx}c &amp;=\\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{c - c}{\\Delta x} \\quad \\text{\u061b \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0644\u0640 $f(x)=c$} \\\\ \\\\\n\n&amp; &amp;=\\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{0}{\\Delta x} = 0\n\n\\end{array}\n\n<\/span><\/span><\/p>\n<h3>\u062f\u0627\u0644\u0629 \u0627\u0644\u0647\u0648\u064a\u0629<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=LudVXLRnmLw&amp;t=169s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = x,<\/span><\/span> \u0641\u0625\u0646:<\/span><\/strong><\/a><\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{df(x)}{dx} =\\frac{dx}{dx}=1<\/span><\/span><\/p>\n<p><span style=\"color: #000080;\"><strong>\u0627\u0644\u0628\u0631\u0647\u0627\u0646:<\/strong><\/span> \u0645\u0634\u0627\u0628\u0647 \u0644\u0644\u063a\u0627\u064a\u0629 \u0644\u0644\u0628\u0631\u0647\u0627\u0646 \u0627\u0644\u0633\u0627\u0628\u0642\u060c \u0648\u064a\u064f\u0633\u062a\u0646\u062a\u062c \u0641\u064a \u062e\u0637\u0648\u0629 \u0648\u0627\u062d\u062f\u0629 \u0643\u0630\u0644\u0643:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rll}\n\n(1) &amp; \\dfrac{d}{dx}x &amp;= \\displaystyle \\lim_{\\Delta x\\to 0} \\dfrac{(x+\\Delta x) - x}{\\Delta x} \\quad \\text{\u061b \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0644\u0640 $f(x) = x$} \\\\ \\\\\n\n&amp; &amp;=\\displaystyle \\lim_{\\Delta x\\to 0} \\dfrac{\\Delta x}{\\Delta x} = 1\n\n\\end{array}\n\n<\/span><\/span><\/p>\n<h3>\u0627\u0644\u0623\u0633\u0633 \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=LudVXLRnmLw&amp;t=239s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0625\u0630\u0627 \u0643\u0627\u0646\u062a <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">f(x) = x^n,<\/span><\/span> \u062d\u064a\u062b<\/span> <\/strong><\/a><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">n<\/span><\/span> \u0639\u062f\u062f\u064b\u0627 \u0637\u0628\u064a\u0639\u064a\u064b\u0627 \u0643\u064a\u0641\u0645\u0627 \u0643\u0627\u0646\u060c \u0641\u0625\u0646\u0647 \u0633\u064a\u0643\u0648\u0646:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{df(x)}{dx} =\\frac{dx^n}{dx} =nx^{n-1}<\/span><\/span><\/p>\n<p><span style=\"color: #000080;\"><strong>\u0627\u0644\u0628\u0631\u0647\u0627\u0646:<\/strong><\/span> \u0644\u0625\u062b\u0628\u0627\u062a \u0647\u0630\u0647 \u0627\u0644\u0645\u0628\u0631\u0647\u0646\u0629\u060c \u064a\u062c\u0628 \u0623\u0646 \u0646\u0633\u062a\u062e\u062f\u0645 <a href=\"https:\/\/toposuranos.com\/ejercicios-de-induccion-matematica-teorema-del-binomio-de-newton\/\" target=\"_blank\" rel=\"noopener\">\u0645\u0628\u0631\u0647\u0646\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646<\/a><\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rll}\n\n(1) &amp;\\displaystyle \\dfrac{d}{dx}x^n = \\lim_{\\Delta x \\to 0} \\frac{(x+\\Delta x)^n -x^n}{\\Delta x} &amp;\\text{ \u061b \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0646\u0647\u0627\u064a\u0629 \u0644\u0640 $f(x)= x^n$} \\\\ \\\\\n\n&amp; \\displaystyle \\phantom{\\displaystyle \\dfrac{d}{dx}x^n} =\\lim_{\\Delta x \\to 0} \\dfrac{\\displaystyle \\left[\\sum_{k=0}^n {{n}\\choose{k}} x^{n-k}(\\Delta x)^{k} \\right] - x^n}{\\Delta x} &amp; \\text{\u061b \u0645\u0628\u0631\u0647\u0646\u0629 \u0630\u0627\u062a \u0627\u0644\u062d\u062f\u064a\u0646 \u0644\u0646\u064a\u0648\u062a\u0646\u060c \u0639\u0644\u0649 (1)} \\\\ \\\\\n\n&amp; \\displaystyle\\phantom{\\displaystyle \\dfrac{d}{dx}x^n} =\\lim_{\\Delta x \\to 0} \\dfrac{\\displaystyle x^n + \\left[\\sum_{k=1}^n {{n}\\choose{k}} x^{n-k}(\\Delta x)^{k} \\right] - x^n}{\\Delta x} &amp; \\text{\u061b \u0641\u0635\u0644 \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0648\u0644 \u0645\u0646 \u0627\u0644\u0645\u062c\u0645\u0648\u0639} \\\\ \\\\\n\n&amp; \\displaystyle\\phantom{\\displaystyle \\dfrac{d}{dx}x^n} =\\lim_{\\Delta x \\to 0} \\dfrac{\\displaystyle \\left[\\sum_{k=1}^n {{n}\\choose{k}} x^{n-k}(\\Delta x)^{k} \\right]}{\\Delta x} &amp; \\text{\u061b \u0625\u0644\u063a\u0627\u0621 \u0627\u0644\u062d\u062f\u0648\u062f \u0627\u0644\u0645\u062a\u0634\u0627\u0628\u0647\u0629} \\\\ \\\\\n\n&amp; \\displaystyle\\phantom{\\displaystyle \\dfrac{d}{dx}x^n} =\\lim_{\\Delta x \\to 0} \\displaystyle \\left[\\sum_{k=1}^n {{n}\\choose{k}} x^{n-k}(\\Delta x)^{k-1} \\right] &amp; \\\\ \\\\\n\n&amp; \\displaystyle\\phantom{\\displaystyle \\dfrac{d}{dx}x^n} =\\lim_{\\Delta x \\to 0} \\displaystyle \\left[ {{n}\\choose{1}} x^{n-1}(\\Delta x)^{0} + \\sum_{k=2}^n {{n}\\choose{k}} x^{n-k}(\\Delta x)^{k-1} \\right] &amp; \\text{\u061b \u0627\u0633\u062a\u062e\u0631\u0627\u062c \u0627\u0644\u062d\u062f \u0627\u0644\u0623\u0648\u0644 \u0645\u0646 \u0627\u0644\u0645\u062c\u0645\u0648\u0639} \\\\ \\\\\n\n&amp; \\displaystyle \\color{blue} {\\displaystyle \\dfrac{d}{dx}x^n} = n x^{n-1} &amp; \\color{black}\n\n\\end{array}\n\n<\/span><\/span><\/p>\n<h3>\u0627\u0644\u0623\u0633\u0633 \u0627\u0644\u0635\u062d\u064a\u062d\u0629<\/h3>\n<p>\u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0627\u0644\u0630\u064a \u062a\u0645 \u0639\u0631\u0636\u0647 \u0644\u0644\u062a\u0648 \u064a\u0628\u0631\u0647\u0646 \u0641\u0642\u0637 \u0639\u0644\u0649 \u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u062a\u064a \u062a\u0643\u0648\u0646 \u0641\u064a\u0647\u0627 \u0627\u0644\u0623\u0633\u0633 \u0623\u0639\u062f\u0627\u062f\u064b\u0627 \u0637\u0628\u064a\u0639\u064a\u0629\u060c \u0648\u0644\u0643\u0646 \u064a\u0645\u0643\u0646 \u062a\u0648\u0633\u064a\u0639\u0647 \u0644\u064a\u0634\u0645\u0644 \u0623\u064a \u0639\u062f\u062f \u0635\u062d\u064a\u062d. \u0625\u0630\u0627 \u0643\u0627\u0646 <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">a\\in \\mathbb{Z}<\/span><\/span>\u060c \u0641\u0625\u0646\u0646\u0627 \u0646\u062d\u0635\u0644 \u0639\u0644\u0649:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{dx^a}{dx} = ax^{a-1}<\/span><\/span><\/p>\n<p>\u0646\u062d\u0646 \u0646\u0639\u0644\u0645 \u0628\u0627\u0644\u0641\u0639\u0644 \u0623\u0646 \u0647\u0630\u0647 \u0627\u0644\u0642\u0627\u0639\u062f\u0629 \u062a\u0646\u062c\u062d \u0641\u064a \u062d\u0627\u0644\u0629 \u0627\u0644\u0623\u0639\u062f\u0627\u062f \u0627\u0644\u0635\u062d\u064a\u062d\u0629 \u0627\u0644\u0645\u0648\u062c\u0628\u0629\u060c \u0644\u0630\u0627 \u064a\u0643\u0641\u064a \u0623\u0646 \u0646\u0631\u0649 \u0645\u0627 \u064a\u062d\u062f\u062b \u0639\u0646\u062f\u0645\u0627 \u0646\u0623\u062e\u0630 \u0623\u0633\u0633\u064b\u0627 \u0633\u0627\u0644\u0628\u0629. \u0648\u0628\u0630\u0644\u0643\u060c \u064a\u0643\u0648\u0646 \u0643\u0627\u0641\u064a\u064b\u0627 \u0623\u0646 \u0646\u0628\u0631\u0647\u0646 \u0623\u0646\u0647 \u064a\u062a\u062d\u0642\u0642:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{dx^{-n}}{dx} = {-n}x^{-n-1}<\/span><\/span><\/p>\n<p><span style=\"color: #000080;\"><strong>\u0627\u0644\u0628\u0631\u0647\u0627\u0646:<\/strong><\/span> \u0644\u0625\u062b\u0628\u0627\u062a \u0630\u0644\u0643\u060c \u064a\u0643\u0641\u064a \u0623\u0646 \u0646\u0623\u062e\u0630 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0643\u0633\u0631:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rll}\n\n(1) &amp; \\dfrac{d}{dx}x^{-n} &amp;= \\dfrac{d}{dx} \\left( \\dfrac{1}{x^n}\\right) \\\\ \\\\\n\n&amp; &amp;= \\dfrac{0 \\cdot nx^{n-1} - nx^{n-1} \\cdot 1}{x^{2n}}\\\\ \\\\\n\n&amp; &amp;= -nx^{n-1-2n} \\\\ \\\\\n\n&amp; &amp;= -nx^{-n-1}\n\n\\end{array}\n\n<\/span><\/span><\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>\u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062a\u0633\u0627\u0645\u064a\u0629<\/h2>\n<h3>\u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=LudVXLRnmLw&amp;t=667s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u062a\u0634\u0645\u0644 \u0647\u0630\u0647 \u0627\u0644\u0642\u0648\u0627\u0639\u062f \u0627\u0644\u062a\u0627\u0644\u064a\u0629<\/span><\/strong><\/a> \u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u062f\u0648\u0627\u0644:<\/p>\n<table>\n<tbody>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dx}\\sin(x) = \\cos(x)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dx}\\sec(x) = \\sec(x)\\tan(x)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dx}\\cos(x) = -\\sin(x)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dx}\\csc(x) = -\\csc(x)\\cot(x)<\/span><\/span><\/td>\n<\/tr>\n<tr>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dx}\\tan(x) = \\sec^2(x)<\/span><\/span><\/td>\n<td><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dx}\\cot(x) = -\\csc^2(x)<\/span><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u0644\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0643\u0644 \u0645\u0646 \u0647\u0630\u0647 \u0627\u0644\u0642\u0648\u0627\u0639\u062f\u060c \u0641\u0625\u0646 \u0623\u0641\u0636\u0644 \u0637\u0631\u064a\u0642 \u0647\u0648 \u0627\u0644\u0628\u062f\u0621 \u0628\u0645\u0634\u062a\u0642\u0627\u062a \u062f\u0627\u0644\u062a\u064a \u0627\u0644\u062c\u064a\u0628 \u0648\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645\u061b \u0648\u0645\u0646 \u062b\u0645\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062c\u0628\u0631 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a\u060c \u064a\u0645\u0643\u0646 \u0627\u0634\u062a\u0642\u0627\u0642 \u0627\u0644\u0642\u0648\u0627\u0639\u062f \u0644\u0628\u0627\u0642\u064a \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629.<\/p>\n<h4>\u0628\u0631\u0647\u0627\u0646 \u0645\u0634\u062a\u0642\u0629 \u062f\u0627\u0644\u0629 \u0627\u0644\u062c\u064a\u0628<\/h4>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp;\\dfrac{d}{dx}\\sin(x) = \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{\\sin(x+\\Delta x) - \\sin(x)}{\\Delta x} &amp; \\text{\u061b \u062a\u0639\u0631\u064a\u0641 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u062c\u064a\u0628} \\\\ \\\\\n\n&amp;\\phantom{\\dfrac{d}{dx}\\sin(x)} = \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{\\sin(x)\\cos(\\Delta x) + \\sin(\\Delta x)\\cos(x) - \\sin(x)}{\\Delta x} &amp; \\\\ \\\\\n\n&amp;\\phantom{\\dfrac{d}{dx}\\sin(x)} = \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{ \\sin(x)\\left[\\cos(\\Delta x) -1\\right] + \\sin(\\Delta x)\\cos(x) }{\\Delta x} &amp; \\\\ \\\\\n\n&amp;\\phantom{\\dfrac{d}{dx}\\sin(x)} = \\displaystyle \\sin(x)\\lim_{\\Delta x \\to 0} \\left[\\dfrac{\\cos(\\Delta x) - 1}{\\Delta x} \\right] + \\cos(x) \\lim_{\\Delta x \\to 0} \\left[ \\dfrac{\\sin(\\Delta x)}{\\Delta x} \\right] &amp; \\\\ \\\\\n\n(2)&amp;\\displaystyle \\lim_{\\Delta x\\to 0} \\dfrac{\\sin(\\Delta x)}{\\Delta x} = 1 &amp; \\text{\u061b \u062d\u0633\u0628 \u0645\u0628\u0631\u0647\u0646\u0629 \u0627\u0644\u062d\u0635\u0631 (Sandwich)}\\\\ \\\\\n\n(3)&amp;\\displaystyle \\lim_{\\Delta x\\to 0} \\dfrac{\\cos(\\Delta x) - 1}{\\Delta x} = \\lim_{\\Delta x\\to 0} \\dfrac{\\cos(\\Delta x) - 1}{\\Delta x} \\cdot \\dfrac{\\cos(\\Delta x) + 1}{\\cos(\\Delta x) + 1} &amp; \\\\ \\\\\n\n&amp;\\displaystyle\\phantom{\\lim_{\\Delta x\\to 0} \\dfrac{\\cos(\\Delta x) - 1}{\\Delta x}} = \\lim_{\\Delta x\\to 0} \\dfrac{\\cos^2(\\Delta x) - 1}{\\Delta x (\\cos(\\Delta x) + 1)} &amp; \\\\ \\\\\n\n&amp;\\displaystyle\\phantom{\\lim_{\\Delta x\\to 0} \\dfrac{\\cos(\\Delta x) - 1}{\\Delta x}} = \\lim_{\\Delta x\\to 0} \\dfrac{-\\sin^2(\\Delta x)}{\\Delta x (\\cos(\\Delta x) + 1)} &amp; \\\\ \\\\\n\n&amp;\\displaystyle\\phantom{\\lim_{\\Delta x\\to 0} \\dfrac{\\cos(\\Delta x) - 1}{\\Delta x}} =- \\lim_{\\Delta x\\to 0} \\dfrac{\\sin(\\Delta x)}{\\Delta x} \\cdot \\lim_{\\Delta x\\to 0} \\dfrac{\\sin(\\Delta x)}{\\cos(\\Delta x) + 1} &amp; \\\\ \\\\\n\n&amp;\\displaystyle\\phantom{\\lim_{\\Delta x\\to 0} \\dfrac{\\cos(\\Delta x) - 1}{\\Delta x}} =- (1)\\cdot(0) = 0 \\\\ \\\\\n\n(4) &amp;\\color{blue}\\dfrac{d}{dx}\\sin(x) = \\cos(x) \\color{black} &amp; \\text{\u061b \u0645\u0646 (1\u060c2\u060c3)}\n\n\\end{array}<\/span><\/span><\/p>\n<h4>\u0628\u0631\u0647\u0627\u0646 \u0645\u0634\u062a\u0642\u0629 \u062f\u0627\u0644\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645<\/h4>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; \\dfrac{d}{dx}\\cos(x) = \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{\\cos(x + \\Delta x) - \\cos(x)}{\\Delta x} &amp; \\text{\u061b \u062a\u0639\u0631\u064a\u0641 \u0645\u0634\u062a\u0642\u0629 \u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645} \\\\ \\\\\n\n&amp; \\phantom{\\dfrac{d}{dx}\\cos(x)} = \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{\\cos(x)\\cos(\\Delta x) - \\sin(x)\\sin(\\Delta x) - \\cos(x)}{\\Delta x} \\\\ \\\\\n\n&amp; \\phantom{\\dfrac{d}{dx}\\cos(x)} = \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{\\cos(x) [ \\cos(\\Delta x) - 1] - \\sin(x)\\sin(\\Delta x)}{\\Delta x}\\\\ \\\\\n\n&amp; \\phantom{\\dfrac{d}{dx}\\cos(x)} = \\cos(x) \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{ [ \\cos(\\Delta x) - 1]}{\\Delta x} - \\sin(x) \\lim_{\\Delta x \\to 0} \\dfrac{\\sin(\\Delta x)}{\\Delta x}\\\\ \\\\\n\n&amp; \\phantom{\\dfrac{d}{dx}\\cos(x)} = \\cos(x) \\cdot(0) - \\sin(x)\\cdot (1)\\\\ \\\\\n\n&amp;\\color{blue}\\dfrac{d}{dx}\\cos(x) = - \\sin(x) \\color{black}\n\n\\end{array}<\/span><\/span><\/p>\n<h4>\u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u0638\u0644\u060c \u0627\u0644\u0642\u0627\u0637\u0639\u060c \u0627\u0644\u0642\u0627\u0637\u0639 \u0627\u0644\u0645\u0639\u0627\u0643\u0633\u060c \u0648\u0627\u0644\u0638\u0644 \u0627\u0644\u0645\u0639\u0627\u0643\u0633<\/h4>\n<p>\u0628\u0645\u0627 \u0623\u0646 \u0644\u062f\u064a\u0646\u0627 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0627\u0644\u062c\u064a\u0628 \u0648\u062c\u064a\u0628 \u0627\u0644\u062a\u0645\u0627\u0645\u060c \u0641\u0625\u0646 \u0627\u0644\u062d\u0635\u0648\u0644 \u0639\u0644\u0649 \u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 \u0627\u0644\u0623\u062e\u0631\u0649 \u064a\u0635\u0628\u062d \u0627\u0644\u0622\u0646 \u0633\u0647\u0644\u064b\u0627 \u0644\u0644\u063a\u0627\u064a\u0629.<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rl}\n\n\\dfrac{d}{dx}\\tan(x) &amp;= \\dfrac{d}{dx} \\left( \\dfrac{\\sin(x)}{\\cos(x)} \\right) = \\dfrac{\\cos^2(x) + \\sin^2(x)}{\\cos^2(x)} = \\dfrac{1}{\\cos^2(x)} = \\color{blue}\\sec^2(x) \\color{black}\\\\ \\\\\n\n\\dfrac{d}{dx}\\sec(x) &amp;= \\dfrac{d}{dx}\\left(\\dfrac{1}{\\cos(x)} \\right) = \\dfrac{\\sin(x)}{\\cos^2(x)} =\\color{blue}\\sec(x)\\tan(x) \\color{black}\\\\ \\\\\n\n\\dfrac{d}{dx}\\csc(x) &amp;= \\dfrac{d}{dx}\\left(\\dfrac{1}{\\cos(x)}\\right) = -\\dfrac{cos(x)}{\\sin^2(x)} =\\color{blue} - \\csc(x)\\cot(x)\\color{black}\\\\ \\\\\n\n\\dfrac{d}{dx} \\cot(x) &amp;= \\dfrac{d}{dx} \\left(\\dfrac{\\cos(x)}{\\sin(x)}\\right) = \\dfrac{-\\sin^2(x)-\\cos^2(x)}{\\sin^2(x)} = -\\dfrac{1}{\\sin^2(x)} =\\color{blue} -\\csc^2(x)\\color{black}\n\n\\end{array}<\/span><\/span><\/p>\n<h3>\u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u064a\u0629<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=LudVXLRnmLw&amp;t=1331s\" target=\"_blank\" rel=\"noopener\"><strong><span style=\"color: #ff0000;\">\u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645 \u0627\u0644\u0637\u0628\u064a\u0639\u064a<\/span><\/strong><\/a> \u062a\u064f\u0639\u0637\u0649 \u0628\u0627\u0644\u0639\u0644\u0627\u0642\u0629 \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\frac{d}{dx}\\ln(x) = \\frac{1}{x}<\/span><\/span><\/p>\n<p><span style=\"color: #000080;\"><strong>\u0627\u0644\u0628\u0631\u0647\u0627\u0646:<\/strong><\/span> \u0627\u0646\u0637\u0644\u0627\u0642\u064b\u0627 \u0645\u0646 \u062a\u0639\u0631\u064a\u0641 \u0627\u0644\u0645\u0634\u062a\u0642\u0629\u060c \u0646\u062d\u0635\u0644 \u0639\u0644\u0649 \u0633\u0644\u0633\u0644\u0629 \u0627\u0644\u062e\u0637\u0648\u0627\u062a \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\begin{array}{rll}\n\n(1) &amp; \\dfrac{d}{dx} \\ln(x) = \\displaystyle \\lim_{\\Delta x \\to 0} \\left [\\dfrac{\\ln(x+\\Delta x) - \\ln(x)}{\\Delta x} \\right] &amp;\\text{\u061b \u062a\u0639\u0631\u064a\u0641 \u0645\u0634\u062a\u0642\u0629 \u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645 \u0627\u0644\u0637\u0628\u064a\u0639\u064a} \\\\ \\\\\n\n&amp; \\phantom{\\dfrac{d}{dx} \\ln(x)} = \\displaystyle \\lim_{\\Delta x \\to 0} \\left[ \\dfrac{1}{\\Delta x} \\ln \\left( \\dfrac{x+\\Delta x}{x} \\right) \\right] \\\\ \\\\\n\n&amp; \\phantom{\\dfrac{d}{dx} \\ln(x)} = \\displaystyle \\lim_{\\Delta x \\to 0} \\left[ \\ln \\left( \\dfrac{x+\\Delta x}{x} \\right)^{\\frac{1}{\\Delta x} } \\right] \\\\ \\\\\n\n&amp; \\phantom{\\dfrac{d}{dx} \\ln(x)} = \\displaystyle \\lim_{\\Delta x \\to 0} \\left[ \\ln \\left( \\dfrac{x+\\Delta x}{x} \\right)^{\\frac{1}{\\color{red}x\\color{black}} \\frac{\\color{red}x\\color{black}}{\\Delta x} } \\right] \\\\ \\\\\n\n&amp; \\phantom{\\dfrac{d}{dx} \\ln(x)} = \\displaystyle \\lim_{\\Delta x \\to 0} \\left[ \\dfrac{1}{x} \\ln \\left( 1 + \\dfrac{\\Delta x}{x} \\right)^{ \\frac{x}{\\Delta x} } \\right] \\\\ \\\\\n\n&amp; \\phantom{\\dfrac{d}{dx} \\ln(x)} =\\dfrac{1}{x} \\ln \\displaystyle \\left[ \\lim_{\\Delta x \\to 0} \\left( 1 + \\dfrac{\\Delta x}{x} \\right)^{ \\frac{x}{\\Delta x} } \\right] \\\\ \\\\\n\n(2) &amp; n=\\dfrac{x}{\\Delta x} &amp; \\text{\u061b \u062a\u0628\u062f\u064a\u0644 \u0645\u062a\u063a\u064a\u0631} \\\\ \\\\\n\n(3) &amp; (\\Delta x \\to 0^+) \\longrightarrow (n\\to +\\infty) \\\\ \\\\\n\n(4) &amp; \\dfrac{d}{dx} \\ln(x) = \\dfrac{1}{x} \\ln\\left[ \\displaystyle \\lim_{n \\to +\\infty} \\left(1 + \\dfrac{1}{n} \\right)^n \\right] = \\dfrac{1}{x} \\ln(e) = \\color{blue}\\dfrac{1}{x} \\color{black} &amp; \\text{\u061b \u0645\u0646 (1\u060c2\u060c3)}\n\n\\end{array}<\/span><\/span><\/p>\n<p>\n\u0628\u0647\u0630\u0627 \u0646\u0643\u0648\u0646 \u0642\u062f \u0627\u0633\u062a\u0639\u0631\u0636\u0646\u0627 \u062e\u0637\u0648\u0629 \u0628\u062e\u0637\u0648\u0629 \u0627\u0644\u0645\u0634\u062a\u0642\u0627\u062a \u0627\u0644\u0623\u0633\u0627\u0633\u064a\u0629 \u0627\u0644\u062a\u064a \u064a\u0646\u0628\u063a\u064a \u0639\u0644\u0649 \u0643\u0644 \u0637\u0627\u0644\u0628 \u0625\u062a\u0642\u0627\u0646\u0647\u0627: \u0645\u0646 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u062c\u0628\u0631\u064a\u0629 \u0627\u0644\u0628\u0633\u064a\u0637\u0629 \u0625\u0644\u0649 \u0623\u0647\u0645 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062a\u0633\u0627\u0645\u064a\u0629 \u0645\u062b\u0644 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 \u0648\u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645 \u0627\u0644\u0637\u0628\u064a\u0639\u064a. \u0645\u0646 \u062e\u0644\u0627\u0644 \u0625\u062a\u0642\u0627\u0646 \u0647\u0630\u0647 \u0627\u0644\u0628\u0631\u0627\u0647\u064a\u0646 \u0633\u062a\u062a\u0645\u0643\u0646 \u0645\u0646 \u062a\u0637\u0628\u064a\u0642 \u0642\u0648\u0627\u0639\u062f \u0627\u0644\u0627\u0634\u062a\u0642\u0627\u0642\u060c \u0648\u0641\u0647\u0645 \u0623\u0635\u0644\u0647\u0627 \u0648\u062a\u0628\u0631\u064a\u0631\u0647\u0627 \u0627\u0644\u0631\u0633\u0645\u064a. \u062a\u064f\u0639\u062f \u0647\u0630\u0647 \u0627\u0644\u0645\u0639\u0631\u0641\u0629 \u0623\u0633\u0627\u0633\u064b\u0627 \u0644\u0645\u0648\u0627\u062c\u0647\u0629 \u0645\u0634\u0643\u0644\u0627\u062a \u0623\u0643\u062b\u0631 \u062a\u0639\u0642\u064a\u062f\u064b\u0627 \u062a\u062a\u0637\u0644\u0628 \u062a\u062d\u0644\u064a\u0644\u064b\u0627 \u062f\u0642\u064a\u0642\u064b\u0627 \u0644\u0644\u062a\u063a\u064a\u0631.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0645\u0634\u062a\u0642\u0627\u062a \u0643\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f \u0648\u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 \u0648\u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645 \u0627\u0644\u0645\u0634\u062a\u0642\u0629 \u0647\u064a \u0623\u062f\u0627\u0629 \u0645\u062d\u0648\u0631\u064a\u0629 \u0641\u064a \u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0641\u0627\u0636\u0644\u060c \u0648\u0644\u0647\u0627 \u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0623\u0633\u0627\u0633\u064a\u0629 \u0641\u064a \u0627\u0644\u0639\u0644\u0648\u0645 \u0648\u0627\u0644\u0647\u0646\u062f\u0633\u0629 \u0648\u0627\u0644\u0627\u0642\u062a\u0635\u0627\u062f. \u064a\u0642\u062f\u0645 \u0647\u0630\u0627 \u0627\u0644\u0645\u0642\u0627\u0644 \u062f\u0644\u064a\u0644\u0627\u064b \u062a\u062f\u0631\u064a\u062c\u064a\u0627\u064b \u0644\u0625\u062a\u0642\u0627\u0646 \u0627\u0634\u062a\u0642\u0627\u0642 \u0627\u0644\u062f\u0648\u0627\u0644\u060c \u0628\u062f\u0621\u064b\u0627 \u0645\u0646 \u0643\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f \u0648\u062d\u062a\u0649 \u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 \u0648\u0627\u0644\u0644\u0648\u063a\u0627\u0631\u064a\u062a\u0645\u064a\u0629. \u0648\u0645\u0646 \u062e\u0644\u0627\u0644 \u0627\u0644\u0628\u0631\u0647\u0627\u0646 \u0648\u0627\u0644\u0623\u0645\u062b\u0644\u0629 \u0627\u0644\u0645\u0644\u0645\u0648\u0633\u0629\u060c \u064a\u0633\u0639\u0649 \u0647\u0630\u0627 \u0627\u0644\u0645\u0642\u0627\u0644 \u0625\u0644\u0649 \u062a\u0648\u0636\u064a\u062d \u0643\u064a\u0641\u064a\u0629 \u062a\u0637\u0628\u064a\u0642 \u0642\u0648\u0627\u0639\u062f \u0627\u0644\u0627\u0634\u062a\u0642\u0627\u0642 \u0648\u0641\u0647\u0645 \u0627\u0644\u0623\u0633\u0627\u0633 \u0627\u0644\u0646\u0638\u0631\u064a \u0644\u0647\u0627. \u0623\u0647\u062f\u0627\u0641 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":33155,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":7,"footnotes":""},"categories":[860,565],"tags":[],"class_list":["post-33394","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-860","category-565"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0645\u0634\u062a\u0642\u0627\u062a \u0643\u062b\u064a\u0631\u0627\u062a \u0627\u0644\u062d\u062f\u0648\u062f \u0648\u0627\u0644\u062f\u0648\u0627\u0644 \u0627\u0644\u0645\u062b\u0644\u062b\u064a\u0629 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