{"id":29722,"date":"2024-11-27T12:00:41","date_gmt":"2024-11-27T12:00:41","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=29722"},"modified":"2024-11-27T17:36:53","modified_gmt":"2024-11-27T17:36:53","slug":"%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%b0%e0%a5%8b%e0%a4%b9-%e0%a4%95%e0%a5%80-%e0%a4%b8%e0%a5%80%e0%a4%ae%e0%a4%be-%e0%a4%95%e0%a5%87-%e0%a4%b0%e0%a5%82%e0%a4%aa-%e0%a4%ae%e0%a5%87%e0%a4%82-%e0%a4%85","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/hi\/%e0%a4%b8%e0%a4%ae%e0%a4%be%e0%a4%b0%e0%a5%8b%e0%a4%b9-%e0%a4%95%e0%a5%80-%e0%a4%b8%e0%a5%80%e0%a4%ae%e0%a4%be-%e0%a4%95%e0%a5%87-%e0%a4%b0%e0%a5%82%e0%a4%aa-%e0%a4%ae%e0%a5%87%e0%a4%82-%e0%a4%85\/","title":{"rendered":"\u0938\u092e\u093e\u0930\u094b\u0939 \u0915\u0940 \u0938\u0940\u092e\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0905\u0935\u0915\u0932\u091c"},"content":{"rendered":"<style>\np {\n    text-align: justify;\n}\n<\/style>\n<h1 style=\"text-align:center;\">\u0938\u092e\u093e\u0915\u0930\u0923 \u0915\u093e \u0938\u0940\u092e\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0905\u0935\u0915\u0932\u091c<\/h1>\n<p style=\"text-align:center;\"><em><strong>\u0938\u093e\u0930\u093e\u0902\u0936:<\/strong><br \/>\n\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902, \u0939\u092e \u0905\u0935\u0915\u0932\u091c \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0947\u0902\u0917\u0947, \u091c\u094b \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0917\u0923\u093f\u0924\u0940\u092f \u0909\u092a\u0915\u0930\u0923 \u0939\u0948\u0964 \u0939\u092e \u090f\u0915 \u0938\u0940\u0915\u0947\u0902\u091f \u0930\u0947\u0916\u093e \u0915\u0940 \u0922\u0932\u093e\u0928 \u0938\u0947 \u0936\u0941\u0930\u0942 \u0915\u0930\u0947\u0902\u0917\u0947 \u0914\u0930 \u091c\u092c \u092c\u093f\u0902\u0926\u0941 \u0938\u092e\u0940\u092a \u0906\u090f\u0902\u0917\u0947, \u0924\u094b \u0939\u092e \u0938\u0940\u092e\u093e \u0932\u0947\u0924\u0947 \u0939\u0941\u090f \u0907\u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e, \u0939\u092e \u0907\u0938\u0915\u0940 \u092e\u0941\u0916\u094d\u092f \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u0913\u0902 \u0914\u0930 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0947\u0902\u0917\u0947, \u091c\u0948\u0938\u0947 \u092f\u094b\u0917, \u0917\u0941\u0923\u093e, \u0914\u0930 \u092d\u093e\u0917 \u0915\u0947 \u0928\u093f\u092f\u092e, \u091c\u094b \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u0914\u0930 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0940 \u0918\u091f\u0928\u093e\u0913\u0902 \u0915\u0947 \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u092e\u0947\u0902 \u0905\u0935\u0915\u0932\u091c \u0915\u094b \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948\u0902\u0964<\/em><\/p>\n<p style=\"text-align:center;\"><strong>\u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0947 \u0909\u0926\u094d\u0926\u0947\u0936\u094d\u092f<\/strong><br \/>\n\u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u0915\u0947 \u0905\u0902\u0924 \u092e\u0947\u0902, \u091b\u093e\u0924\u094d\u0930 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0902\u0917\u0947:\n<\/p>\n<ol>\n<li><strong>\u0938\u092e\u091d\u0928\u093e:<\/strong> \u0905\u0935\u0915\u0932\u091c \u0915\u094b \u090f\u0915 \u0938\u0940\u092e\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u091c\u094b \u090f\u0915 \u0915\u093e\u0930\u094d\u092f \u092e\u0947\u0902 \u0924\u093e\u0924\u094d\u0915\u093e\u0932\u093f\u0915 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u093e \u0935\u0930\u094d\u0923\u0928 \u0915\u0930\u0924\u093e \u0939\u0948 \u0914\u0930 \u090f\u0915 \u0935\u0915\u094d\u0930 \u092a\u0930 \u090f\u0915 \u092c\u093f\u0902\u0926\u0941 \u092a\u0930 \u0938\u094d\u092a\u0930\u094d\u0936 \u0930\u0947\u0916\u093e \u0915\u0940 \u0922\u0932\u093e\u0928 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902\u0964<\/li>\n<li><strong>\u0938\u092e\u091d\u093e\u0928\u093e:<\/strong> \u0915\u093f \u0905\u0935\u0915\u0932\u0928\u0940\u092f\u0924\u093e \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u0924\u0924\u0924\u093e \u0915\u094b \u0915\u0948\u0938\u0947 \u092a\u094d\u0930\u092d\u093e\u0935\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964<\/li>\n<li><strong>\u092a\u094d\u0930\u0926\u0930\u094d\u0936\u093f\u0924 \u0915\u0930\u0928\u093e:<\/strong> \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0938\u0947 \u0905\u0935\u0915\u0932\u0928 \u0915\u0947 \u092e\u0942\u0932\u092d\u0942\u0924 \u0928\u093f\u092f\u092e\u0964<\/li>\n<li><strong>\u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u093e:<\/strong> \u0905\u0935\u0915\u0932\u091c \u0915\u0947 \u092c\u0940\u091c\u0917\u0923\u093f\u0924\u0940\u092f \u0917\u0941\u0923 (\u092f\u094b\u0917, \u0917\u0941\u0923\u093e, \u092d\u093e\u0917) \u0915\u093e \u0917\u0923\u093f\u0924\u0940\u092f \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u092e\u0947\u0902\u0964<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong><u>\u0935\u093f\u0937\u092f\u0935\u0938\u094d\u0924\u0941 \u0938\u0942\u091a\u0915\u093e\u0902\u0915:<\/u><\/strong><br \/>\n<a href=\"#1\"><strong>\u0905\u0935\u0915\u0932\u091c \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e<\/strong><\/a><br \/>\n<a href=\"#1\">\u0938\u0940\u0915\u0947\u0902\u091f \u0930\u0947\u0916\u093e \u0915\u0940 \u0922\u0932\u093e\u0928<\/a><br \/>\n<a href=\"#1\">\u0938\u0940\u092e\u093e \u0915\u0947 \u092a\u093e\u0938 \u091c\u093e\u0928\u093e: \u0905\u0935\u0915\u0932\u091c \u0914\u0930 \u0938\u094d\u092a\u0930\u094d\u0936 \u0930\u0947\u0916\u093e \u0915\u0940 \u0922\u0932\u093e\u0928<\/a><br \/>\n<a href=\"#1\">\u0935\u0948\u0915\u0932\u094d\u092a\u093f\u0915 \u092a\u0930\u093f\u092d\u093e\u0937\u093e<\/a><br \/>\n<a href=\"#1\"><strong>\u0905\u0935\u0915\u0932\u091c \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u090f\u0901<\/strong><\/a><br \/>\n<a href=\"#1\">\u0905\u0935\u0915\u0932\u0928\u0940\u092f\u0924\u093e \u0938\u0947 \u0938\u0924\u0924\u0924\u093e \u0915\u093e \u0938\u0902\u0915\u0947\u0924 \u092e\u093f\u0932\u0924\u093e \u0939\u0948<\/a><br \/>\n<a href=\"#1\">\u0905\u0935\u0915\u0932\u091c \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/TFxATgmYvkY\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><\/p>\n<p><a name=\"1\"><\/a><\/p>\n<h2>\u0905\u0935\u0915\u0932\u091c \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e<\/h2>\n<p>\u092a\u094d\u0930\u0915\u0943\u0924\u093f \u0938\u093e\u092e\u093e\u0928\u094d\u092f\u0924\u0903 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928\u0936\u0940\u0932 \u0939\u094b\u0924\u0940 \u0939\u0948, \u0914\u0930 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u0940 \u0917\u0923\u0928\u093e \u0914\u0930 \u0938\u092e\u091d \u0915\u0947 \u0932\u093f\u090f \u092e\u0941\u0916\u094d\u092f \u0917\u0923\u093f\u0924\u0940\u092f \u0909\u092a\u0915\u0930\u0923 \u0905\u0935\u0915\u0932\u091c \u0939\u0948\u0964 \u092f\u0939 \u092a\u094d\u0930\u0936\u094d\u0928 \u0915\u0930\u0928\u0947 \u0938\u0947 \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u0939\u094b\u0924\u093e \u0939\u0948, \u00ab\u091c\u092c \u091a\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0915\u094b \u090f\u0915 \u092c\u0939\u0941\u0924 \u091b\u094b\u091f\u0940 \u092e\u093e\u0924\u094d\u0930\u093e <span class=\"katex-eq\" data-katex-display=\"false\">\\Delta x<\/span> \u0938\u0947 \u092c\u0922\u093c\u093e\u092f\u093e \u092f\u093e \u0918\u091f\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u0924\u094b \u0915\u093e\u0930\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0915\u093e \u092e\u093e\u0928 \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u093e?\u00bb\u0964 \u0907\u0938 \u092a\u094d\u0930\u0936\u094d\u0928 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0924\u0947 \u0939\u0941\u090f \u0915\u093e\u0930\u094d\u092f \u0915\u0940 \u0938\u0940\u092e\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0905\u0935\u0915\u0932\u091c \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0909\u092d\u0930\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h3>\u0938\u0940\u0915\u0947\u0902\u091f \u0930\u0947\u0916\u093e \u0915\u0940 \u0922\u0932\u093e\u0928<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=164s\" target=\"_blank\" rel=\"noopener\"><strong>\u092e\u093e\u0928 \u0932\u0947\u0902 \u090f\u0915 \u0915\u093e\u0930\u094d\u092f<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0915\u094b \u0926\u094b \u092c\u093f\u0902\u0926\u0941\u0913\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">x_0 + \\Delta x<\/span> \u092a\u0930\u0964 \u0915\u094b\u0908 \u092d\u0940 \u0930\u0947\u0916\u093e \u091c\u094b \u0935\u0915\u094d\u0930 \u0915\u0947 \u0926\u094b \u092c\u093f\u0902\u0926\u0941\u0913\u0902 \u0915\u094b \u0915\u093e\u091f\u0924\u0940 \u0939\u0948, \u00ab\u0938\u0940\u0915\u0947\u0902\u091f \u0930\u0947\u0916\u093e\u00bb \u0915\u0939\u0932\u093e\u0924\u0940 \u0939\u0948, \u0914\u0930 \u092f\u0939 \u091a\u093f\u0924\u094d\u0930 \u092e\u0947\u0902 \u0926\u093f\u0916\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/--KZ1YA55iug\/YI_jLiez_RI\/AAAAAAAAFCs\/xYcWyzwUaf88McAiTNK7l6tOSZQKyZFdwCLcBGAsYHQ\/s0\/graficosecante.PNG\" alt=\"\u0938\u0940\u0915\u0947\u0902\u091f \u0930\u0947\u0916\u093e \u0915\u093e \u0917\u094d\u0930\u093e\u092b\" class=\" aligncenter lazyload\" width=\"397\" height=\"233\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/--KZ1YA55iug\/YI_jLiez_RI\/AAAAAAAAFCs\/xYcWyzwUaf88McAiTNK7l6tOSZQKyZFdwCLcBGAsYHQ\/s0\/graficosecante.PNG\" alt=\"\u0938\u0940\u0915\u0947\u0902\u091f \u0930\u0947\u0916\u093e \u0915\u093e \u0917\u094d\u0930\u093e\u092b\" class=\" aligncenter lazyload\" width=\"397\" height=\"233\" \/><\/noscript><\/p>\n<p>\u0907\u0938 \u0935\u093f\u0936\u0947\u0937 \u0938\u0940\u0915\u0947\u0902\u091f \u0930\u0947\u0916\u093e \u0915\u0940 \u0922\u0932\u093e\u0928 \u0939\u094b\u0924\u0940 \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{\\Delta f(x_0)}{\\Delta x} = \\dfrac{f(x_0 + \\Delta x) - f(x_0)}{\\Delta x}<\/span>\n<p><a name=\"3\"><\/a><\/p>\n<h3>\u0938\u0940\u092e\u093e \u0915\u0947 \u092a\u093e\u0938 \u091c\u093e\u0928\u093e: \u0905\u0935\u0915\u0932\u091c \u0914\u0930 \u0938\u094d\u092a\u0930\u094d\u0936 \u0930\u0947\u0916\u093e \u0915\u0940 \u0922\u0932\u093e\u0928<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=278s\" target=\"_blank\" rel=\"noopener\"><strong>\u092f\u0926\u093f \u0939\u092e \u0935\u0915\u094d\u0930<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">y=f(x)<\/span> \u0915\u0940 \u0938\u0940\u0915\u0947\u0902\u091f \u0930\u0947\u0916\u093e \u0915\u094b \u0926\u0947\u0916\u0947\u0902, \u091c\u094b <span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">x_0 + \\Delta x<\/span> \u0938\u0947 \u0917\u0941\u091c\u0930\u0924\u0940 \u0939\u0948, \u0914\u0930 \u092b\u093f\u0930 \u0938\u0940\u092e\u093e \u0932\u0947\u0902 \u091c\u092c <span class=\"katex-eq\" data-katex-display=\"false\">\\Delta x<\/span> \u0936\u0942\u0928\u094d\u092f \u0915\u0940 \u0913\u0930 \u091c\u093e\u0924\u093e \u0939\u0948, \u0924\u094b \u0939\u092e\u0947\u0902 \u0935\u0915\u094d\u0930 \u092a\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">(x_0, f(x_0))<\/span> \u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0917\u0941\u091c\u0930\u0928\u0947 \u0935\u093e\u0932\u0940 \u0938\u094d\u092a\u0930\u094d\u0936 \u0930\u0947\u0916\u093e \u092e\u093f\u0932\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-8wCxY7adTBw\/YI_kfLeezzI\/AAAAAAAAFC0\/o6nKbRKv1SISYU3Rx7ML5Rly29edqey3ACLcBGAsYHQ\/s0\/grafico%2Brecta%2Btangente.PNG\" alt=\"\u0938\u094d\u092a\u0930\u094d\u0936 \u0930\u0947\u0916\u093e \u0915\u093e \u0917\u094d\u0930\u093e\u092b\" class=\" aligncenter lazyload\" width=\"464\" height=\"268\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-8wCxY7adTBw\/YI_kfLeezzI\/AAAAAAAAFC0\/o6nKbRKv1SISYU3Rx7ML5Rly29edqey3ACLcBGAsYHQ\/s0\/grafico%2Brecta%2Btangente.PNG\" alt=\"\u0938\u094d\u092a\u0930\u094d\u0936 \u0930\u0947\u0916\u093e \u0915\u093e \u0917\u094d\u0930\u093e\u092b\" class=\" aligncenter lazyload\" width=\"464\" height=\"268\" \/><\/noscript><\/p>\n<p>\u0907\u0938\u0938\u0947 \u0939\u092e\u0947\u0902 \u0915\u093e\u0930\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0915\u0947 \u0915\u093f\u0938\u0940 \u092c\u093f\u0902\u0926\u0941 <span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span> \u092a\u0930 \u0905\u0935\u0915\u0932\u091c \u0915\u0940 \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u092e\u093f\u0932\u0924\u0940 \u0939\u0948, \u091c\u094b \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\dfrac{df(x_0)}{dx}:= \\lim_{\\Delta x \\to 0}\\dfrac{\\Delta f(x_0)}{\\Delta x} = \\lim_{\\Delta x \\to 0} \\dfrac{f(x_0 + \\Delta x) - f(x_0)}{\\Delta x}<\/span>\n<p>\u092f\u0939 \u092a\u0930\u093f\u092d\u093e\u0937\u093e <span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span> \u092a\u0930 \u0935\u0915\u094d\u0930 \u0915\u0947 \u0938\u094d\u092a\u0930\u094d\u0936 \u0930\u0947\u0916\u093e \u0915\u0940 \u0922\u0932\u093e\u0928 \u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0928\u093f\u0927\u093f\u0924\u094d\u0935 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964<\/p>\n<p><a name=\"4\"><\/a><\/p>\n<h3>\u0935\u0948\u0915\u0932\u094d\u092a\u093f\u0915 \u092a\u0930\u093f\u092d\u093e\u0937\u093e<\/h3>\n<p>\u0905\u0935\u0915\u0932\u091c \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0915\u094b \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930\u0928\u0947 \u0915\u093e \u090f\u0915 \u0935\u0948\u0915\u0932\u094d\u092a\u093f\u0915 \u0924\u0930\u0940\u0915\u093e \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092a\u094d\u0930\u0924\u093f\u0938\u094d\u0925\u093e\u092a\u0928 \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\nx_i &amp;= x_0\\\\\n\nx_f &amp;= x_i + \\Delta x\n\n\\end{array}\n\n<\/span>\n<p>\u0907\u0938\u0938\u0947 \u0939\u092e\u0947\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">\\Delta x = x_f - x_i<\/span> \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948, \u0914\u0930 \u0905\u0935\u0915\u0932\u091c \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0907\u0938 \u0930\u0942\u092a \u092e\u0947\u0902 \u0939\u094b \u091c\u093e\u0924\u0940 \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\displaystyle \\dfrac{df(x_i)}{dx} &amp;=\\displaystyle \\lim_{\\Delta x \\to 0}\\dfrac{ f(x_i + \\Delta x) - f(x_i)}{\\Delta x}\\\\ \\\\\n\n&amp;=\\displaystyle \\lim_{x_f - x_i \\to 0} \\dfrac{f(x_f) - f(x_i)}{x_f - x_i}\\\\ \\\\\n\n&amp;=\\displaystyle  \\lim_{x_f \\to x_i } \\dfrac{f(x_f) - f(x_i)}{x_f - x_i}\n\n\\end{array}\n\n<\/span>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-GLyWOue8OUs\/YJAHOc_lTOI\/AAAAAAAAFC8\/3IV-onfsq9QC4nyweccS4ZN_O-JlWVz8wCLcBGAsYHQ\/s0\/definicion%2Bderivada%2Bcomo%2Blimite.PNG\" alt=\"\u0905\u0935\u0915\u0932\u091c \u0915\u0940 \u0938\u0940\u092e\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093e\" class=\" aligncenter lazyload\" width=\"469\" height=\"243\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-GLyWOue8OUs\/YJAHOc_lTOI\/AAAAAAAAFC8\/3IV-onfsq9QC4nyweccS4ZN_O-JlWVz8wCLcBGAsYHQ\/s0\/definicion%2Bderivada%2Bcomo%2Blimite.PNG\" alt=\"\u0905\u0935\u0915\u0932\u091c \u0915\u0940 \u0938\u0940\u092e\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093e\" class=\" aligncenter lazyload\" width=\"469\" height=\"243\" \/><\/noscript><\/p>\n<p>\u0926\u094b\u0928\u094b\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093e\u090f\u0901 \u0938\u092e\u093e\u0928 \u0939\u0948\u0902 \u0914\u0930 \u0938\u0941\u0935\u093f\u0927\u093e \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u0907\u0928\u092e\u0947\u0902 \u0938\u0947 \u0915\u093f\u0938\u0940 \u0915\u093e \u092d\u0940 \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<p><a name=\"5\"><\/a><\/p>\n<h2>\u0905\u0935\u0915\u0932\u091c \u0915\u0940 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u090f\u0901<\/h2>\n<p>\u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0915\u094b\u0908 \u0915\u093e\u0930\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span> \u092a\u0930 \u0905\u0935\u0915\u0932\u0928\u0940\u092f \u0939\u0948, \u091c\u092c \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0940\u092e\u093e \u092e\u094c\u091c\u0942\u0926 \u0939\u094b:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{f(x_0 + \\Delta x) - f(x_0)}{\\Delta x}<\/span>\n<p>\u0914\u0930 \u0939\u092e \u0915\u0939\u0947\u0902\u0917\u0947 \u0915\u093f \u092f\u0939 \u0915\u093f\u0938\u0940 \u0938\u0947\u091f <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u092e\u0947\u0902 \u0905\u0935\u0915\u0932\u0928\u0940\u092f \u0939\u0948, \u092f\u0926\u093f \u0938\u0940\u092e\u093e <span class=\"katex-eq\" data-katex-display=\"false\">x_0 \\in I<\/span> \u0915\u0947 \u0932\u093f\u090f \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0939\u094b\u0964 \u0905\u0935\u0915\u0932\u0928\u0940\u092f \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u092e\u0947\u0902 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0935\u093f\u0936\u0947\u0937\u0924\u093e\u090f\u0901 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902:<\/p>\n<p><a name=\"6\"><\/a><\/p>\n<h3>\u0905\u0935\u0915\u0932\u0928\u0940\u092f\u0924\u093e \u0938\u0924\u0924\u0924\u093e \u0915\u094b \u0907\u0902\u0917\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948<\/h3>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=526s\" target=\"_blank\" rel=\"noopener\"><strong>\u092f\u0926\u093f \u0915\u094b\u0908 \u0915\u093e\u0930\u094d\u092f<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span> \u092a\u0930 \u0905\u0935\u0915\u0932\u0928\u0940\u092f \u0939\u0948, \u0924\u094b \u0935\u0939 <span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span> \u092a\u0930 \u0938\u0924\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0947 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0924\u0930\u094d\u0915 \u0938\u0947 \u0938\u093f\u0926\u094d\u0927 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:<\/p>\n<p>\u0915\u093f\u0938\u0940 \u0915\u093e\u0930\u094d\u092f <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0915\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span> \u092a\u0930 \u0938\u0924\u0924 \u0939\u094b\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092f\u0939 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0}f(x) = f(x_0)<\/span>\n<p>\u092f\u0926\u093f \u0939\u092e \u0907\u0938 \u0905\u092d\u093f\u0935\u094d\u092f\u0915\u094d\u0924\u093f \u0915\u0947 \u092c\u093e\u090f\u0901 \u092d\u093e\u0917 \u0915\u0940 \u091c\u093e\u0902\u091a \u0915\u0930\u0947\u0902, \u0924\u094b \u0939\u092e\u0947\u0902 \u092e\u093f\u0932\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\displaystyle \\lim_{x\\to x_0} f(x) &amp;= \\displaystyle \\lim_{x\\to x_0} \\left[ f(x) + f(x_0) - f(x_0) \\right] \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{x\\to x_0} \\left[f(x_0) + \\left( f(x)  - f(x_0) \\right) \\right] \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{x\\to x_0} \\left[f(x_0) + \\left( \\dfrac{f(x)  - f(x_0)}{x- x_0} \\right)(x-x_0)  \\right] \\\\ \\\\\n\n&amp;=f(x_0) +\\displaystyle \\lim_{x\\to x_0} \\left[ \\left( \\dfrac{f(x)  - f(x_0)}{x- x_0} \\right)(x-x_0) \\right] \\\\ \\\\\n\n\\end{array}\n\n<\/span>\n<p>\u0907\u0938\u0938\u0947 \u0939\u092e \u092a\u093e\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f, <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> \u0915\u0947 <span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span> \u092a\u0930 \u0938\u0924\u0924 \u0939\u094b\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948 \u0915\u093f \u0926\u093e\u090f\u0901 \u092d\u093e\u0917 \u0915\u0940 \u0938\u0940\u092e\u093e \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0939\u094b\u0964 \u092f\u0939 \u0924\u092d\u0940 \u0938\u0902\u092d\u0935 \u0939\u0948, \u091c\u092c:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\displaystyle \\lim_{x\\to x_0} \\dfrac{f(x) - f(x_0)}{x-x_0} =\\dfrac{df(x_0)}{dx}<\/span>\n<p>\u0926\u0942\u0938\u0930\u0947 \u0936\u092c\u094d\u0926\u094b\u0902 \u092e\u0947\u0902, \u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span> \u092a\u0930 \u0905\u0935\u0915\u0932\u0928\u0940\u092f \u0939\u0948\u0964 \u0905\u0924\u0903 \u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">f(x)<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">x_0<\/span> \u092a\u0930 \u0905\u0935\u0915\u0932\u0928\u0940\u092f \u0939\u0948, \u0924\u094b \u092f\u0939 \u0909\u0938 \u092c\u093f\u0902\u0926\u0941 \u092a\u0930 \u0938\u0924\u0924 \u0939\u094b\u0917\u093e\u0964<\/p>\n<p><a name=\"7\"><\/a><\/p>\n<h3>\u0905\u0935\u0915\u0932\u091c \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924<\/h3>\n<p>\u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">f<\/span> \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> <span class=\"katex-eq\" data-katex-display=\"false\">I<\/span> \u092e\u0947\u0902 \u0938\u092d\u0940 <span class=\"katex-eq\" data-katex-display=\"false\">x<\/span> \u0915\u0947 \u0932\u093f\u090f \u0905\u0935\u0915\u0932\u0928\u0940\u092f \u0939\u0948\u0902, \u0914\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\alpha,\\beta \\in \\mathbb{R}<\/span>, \u0924\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0924\u094d\u092f \u0939\u094b\u0917\u093e:<\/p>\n<ol>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dx} \\left( \\alpha f(x) \\pm \\beta g(x) \\right) = \\alpha \\dfrac{df(x)}{dx} \\pm \\beta\\dfrac{dg(x)}{dx}<\/span><\/li>\n<li><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dx} \\left( f(x) g(x) \\right) = \\dfrac{df(x)}{dx}g(x) + f(x)\\dfrac{dg(x)}{dx}<\/span><\/li>\n<li>\u092f\u0926\u093f <span class=\"katex-eq\" data-katex-display=\"false\">g(x) \\neq 0<\/span>, \u0924\u094b <span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{d}{dx} \\left( \\dfrac{f(x)}{g(x)} \\right) = \\dfrac{\\dfrac{df(x)}{dx}g(x) - f(x)\\dfrac{dg(x)}{dx}}{\\left[g(x)\\right]^2}<\/span><\/li>\n<\/ol>\n<p>\u091c\u0948\u0938\u093e \u0915\u093f \u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u0905\u0935\u0915\u0932\u091c \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924 \u092a\u0939\u0932\u0947 \u092a\u0939\u0932 \u091c\u093f\u0924\u0928\u093e \u0938\u0939\u091c \u092a\u094d\u0930\u0924\u0940\u0924 \u0939\u094b\u0924\u093e \u0939\u0948, \u0909\u0924\u0928\u093e \u0938\u0930\u0932 \u0928\u0939\u0940\u0902 \u0939\u0948; \u0939\u093e\u0932\u093e\u0901\u0915\u093f, \u0907\u0928 \u0917\u0941\u0923\u094b\u0902 \u0915\u093e \u092a\u094d\u0930\u092e\u093e\u0923 \u0914\u092a\u091a\u093e\u0930\u093f\u0915 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u0938\u0947 \u0905\u0927\u093f\u0915 \u0915\u0920\u093f\u0928\u093e\u0908 \u0915\u0947 \u092c\u093f\u0928\u093e \u0928\u093f\u0915\u093e\u0932\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<p><span style=\"color: #000080;\">\u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924:<\/span><\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=925s\" target=\"_blank\" rel=\"noopener\"><strong>\u0938\u0902\u091a\u092f\u0928 \u0915\u0947 \u0905\u0935\u0915\u0932\u091c \u0915\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924<\/strong><\/a> \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0924\u0930\u094d\u0915 \u0915\u093e \u092a\u093e\u0932\u0928 \u0915\u0930\u0915\u0947 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\dfrac{d}{dx}\\left(\\alpha f(x) \\pm \\beta g(x) \\right) &amp; =\\displaystyle \\lim_{\\Delta x\\to 0} \\dfrac{\\left[\\alpha f(x+\\Delta x) \\pm \\beta g(x+ \\Delta x)\\right] - \\left[\\alpha f(x) \\pm \\beta g(x) \\right]}{\\Delta x} \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{ \\left[\\alpha f(x+\\Delta x) - \\alpha f(x)\\right] \\pm \\left[\\beta g(x+\\Delta x) - \\beta g(x)\\right]}{\\Delta x} \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{ \\alpha \\left[ f(x+\\Delta x) -  f(x)\\right] \\pm  \\beta  \\left[ g(x+\\Delta x) - g(x)\\right]}{\\Delta x} \\\\ \\\\\n\n&amp;= \\displaystyle \\alpha \\lim_{\\Delta x \\to 0} \\dfrac{f(x+\\Delta x) -  f(x)}{\\Delta x} \\pm \\beta \\lim_{\\Delta x \\to 0} \\dfrac{ g(x+\\Delta x) -  g(x)}{\\Delta x} \\\\ \\\\\n\n&amp;= \\alpha \\dfrac{df(x)}{dx} \\pm \\beta \\dfrac{dg(x)}{dx}\n\n\\end{array}\n\n<\/span>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=1059s\" target=\"_blank\" rel=\"noopener\"><strong>\u0917\u0941\u0923\u093e \u0915\u0947 \u0905\u0935\u0915\u0932\u091c \u0915\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924<\/strong><\/a> \u0925\u094b\u0921\u093c\u093e \u0905\u0927\u093f\u0915 \u091c\u091f\u093f\u0932 \u0939\u0948, \u0932\u0947\u0915\u093f\u0928 \u0938\u092e\u091d\u0928\u0947 \u092f\u094b\u0917\u094d\u092f \u0939\u0948:<\/p>\n<p style=\"text-align:center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\dfrac{d}{dx}\\left[f(x)g(x)\\right] &amp;= \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{f(x+\\Delta x) g(x+\\Delta x) -  f(x) g(x)}{\\Delta x} \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{f(x+\\Delta x) g(x+\\Delta x) + \\color{red}f(x)g(x+\\Delta x) - f(x)g(x+\\Delta x) \\color{black} - f(x) g(x)}{\\Delta x} \\\\ \\\\\n\n&amp;= \\displaystyle \\lim_{\\Delta x \\to 0} \\dfrac{\\left[f(x+\\Delta x) - f(x) \\right] g(x+\\Delta x) + f(x) \\left[g(x+\\Delta x)  - g(x)\\right]}{\\Delta x} \\\\ \\\\\n\n&amp;=\\displaystyle \\lim_{\\Delta x \\to 0} g(x+\\Delta x) \\dfrac{f(x+\\Delta x) - f(x)}{\\Delta x} + f(x)\\lim_{\\Delta x \\to 0} \\dfrac{g(x+\\Delta x) - g(x)}{\\Delta x}\\\\ \\\\\n\n&amp;=\\displaystyle \\lim_{\\Delta x \\to 0} g(x+\\Delta x)\\lim_{\\Delta x \\to 0} \\dfrac{f(x+\\Delta x) - f(x)}{\\Delta x} + f(x)\\lim_{\\Delta x \\to 0} \\dfrac{g(x+\\Delta x) - g(x)}{\\Delta x}\\\\ \\\\\n\n&amp;= g(x) \\dfrac{df(x)}{dx} + f(x)\\dfrac{dg(x)}{dx}\n\n\\end{array}\n\n<\/span>\n<p>\u092f\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">g<\/span> \u0915\u094b \u0938\u0924\u0924 \u092e\u093e\u0928\u0915\u0930 <span class=\"katex-eq\" data-katex-display=\"false\">\\lim_{\\Delta x\\to 0 } g(x+\\Delta x) = g(x)<\/span> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u0914\u0930 \u092b\u093f\u0930 <strong>\u0938\u0940\u092e\u093e\u0913\u0902 \u0915\u093e \u092c\u0940\u091c\u0917\u0923\u093f\u0924<\/strong> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 \u0915\u094b \u0938\u093f\u0926\u094d\u0927 \u0915\u093f\u092f\u093e \u0917\u092f\u093e\u0964<\/p>\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=TFxATgmYvkY&amp;t=162s\" target=\"_blank\" rel=\"noopener\"><strong>\u0905\u0902\u0924 \u092e\u0947\u0902, \u092d\u093e\u0917 \u0915\u0947 \u0905\u0935\u0915\u0932\u091c \u0915\u093e \u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924<\/strong><\/a> \u0917\u0941\u0923\u093e \u0915\u0947 \u092a\u0930\u093f\u0923\u093e\u092e \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0938\u093f\u0926\u094d\u0927 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964 \u092e\u093e\u0928 \u0932\u0947\u0902 <span class=\"katex-eq\" data-katex-display=\"false\">k(x) = f(x)\/g(x)<\/span>, \u091c\u0939\u093e\u0901 <span class=\"katex-eq\" data-katex-display=\"false\">g(x)\\neq 0<\/span>\u0964 \u0907\u0938\u0915\u0947 \u092a\u0930\u093f\u0923\u093e\u092e\u0938\u094d\u0935\u0930\u0942\u092a:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\dfrac{df(x)}{dx}= \\dfrac{d}{dx}(k(x)g(x)) = \\dfrac{dk(x)}{dx}g(x) + k(x)\\dfrac{dg(x)}{dx}<\/span>\n<p>\u0905\u092c <span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{dk(x)}{dx}<\/span> \u0915\u094b \u0939\u0932 \u0915\u0930\u0947\u0902:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\dfrac{dk(x)}{dx}g(x) = \\dfrac{df(x)}{dx} - k(x)\\dfrac{dg(x)}{dx} = \\dfrac{d}{dx}f(x) - \\dfrac{f(x)}{g(x)}\\dfrac{dg(x)}{dx} <\/span>\n<p>\u0914\u0930 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\n\\begin{array}{rl}\n\n\\dfrac{d}{dx}\\left(\\dfrac{f(x)}{g(x)}\\right)\n\n &amp;= \\dfrac{dk(x)}{dx} =\\dfrac{1}{g(x)} \\dfrac{df(x)}{dx} - \\dfrac{f(x)}{\\left[g(x)\\right]^2}\\dfrac{dg(x)}{dx} \\\\ \\\\\n\n&amp; = \\dfrac{\\dfrac{df(x)}{dx}g(x) - f(x) \\dfrac{dg(x)}{dx}}{[g(x)]^2}\n\n\\end{array}\n\n<\/span>\n<p>\u092f\u0939 \u0935\u0939\u0940 \u0939\u0948 \u091c\u093f\u0938\u0947 \u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0925\u093e\u0964<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0938\u092e\u093e\u0915\u0930\u0923 \u0915\u093e \u0938\u0940\u092e\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0905\u0935\u0915\u0932\u091c \u0938\u093e\u0930\u093e\u0902\u0936: \u0907\u0938 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902, \u0939\u092e \u0905\u0935\u0915\u0932\u091c \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0947\u0902\u0917\u0947, \u091c\u094b \u0915\u093e\u0930\u094d\u092f\u094b\u0902 \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u093e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u0917\u0923\u093f\u0924\u0940\u092f \u0909\u092a\u0915\u0930\u0923 \u0939\u0948\u0964 \u0939\u092e \u090f\u0915 \u0938\u0940\u0915\u0947\u0902\u091f \u0930\u0947\u0916\u093e \u0915\u0940 \u0922\u0932\u093e\u0928 \u0938\u0947 \u0936\u0941\u0930\u0942 \u0915\u0930\u0947\u0902\u0917\u0947 \u0914\u0930 \u091c\u092c \u092c\u093f\u0902\u0926\u0941 \u0938\u092e\u0940\u092a \u0906\u090f\u0902\u0917\u0947, \u0924\u094b \u0939\u092e \u0938\u0940\u092e\u093e \u0932\u0947\u0924\u0947 \u0939\u0941\u090f \u0907\u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947\u0964 \u0907\u0938\u0915\u0947 \u0905\u0932\u093e\u0935\u093e, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":29706,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":0,"footnotes":""},"categories":[862,577],"tags":[],"class_list":["post-29722","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-862","category-577"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>\u0938\u092e\u093e\u0930\u094b\u0939 \u0915\u0940 \u0938\u0940\u092e\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0905\u0935\u0915\u0932\u091c - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"\u092e\u0948\u0902 \u0906\u092a\u0915\u094b \u0938\u092e\u093e\u0930\u094b\u0939 \u0915\u0940 \u0938\u0940\u092e\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0905\u0935\u0915\u0932\u091c \u0915\u0940 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