{"id":1938,"date":"2019-03-15T11:56:16","date_gmt":"2019-03-15T02:56:16","guid":{"rendered":"https:\/\/sasamath.com\/wp\/?p=1938"},"modified":"2019-09-05T19:48:46","modified_gmt":"2019-09-05T10:48:46","slug":"calculus-definition-of-a-derivative","status":"publish","type":"post","link":"https:\/\/sasamath.com\/blog\/articles\/calculus-definition-of-a-derivative\/","title":{"rendered":"\ubbf8\ubd84\uc758 \uc815\uc758"},"content":{"rendered":"<p>\ud568\uc218 \\(y=f(x)\\)\uc758 \uadf8\ub798\ud504\uac00 \ubfb0\uc871\ud55c \ubd80\ubd84\uc774 \uc5c6\uace0 \ub9e4\ub044\ub7fd\uac8c \uc774\uc5b4\uc838 \uc788\uc744 \ub54c \uadf8\ub798\ud504 \uc704\uc758 \ud55c \uc810\uc5d0\uc11c \uc811\uc120\uc744 \uc0dd\uac01\ud560 \uc218 \uc788\ub2e4. \uc774 \uc811\uc120\uc758 \uae30\uc6b8\uae30\ub294 \uc811\uc810 \uadfc\ucc98\uc5d0\uc11c \\(x\\)\uc758 \ubcc0\ud654\ub7c9\uacfc \\(y\\)\uc758 \ubcc0\ud654\ub7c9\uc758 \ube44\uc758 \uadf9\ud55c\uac12\uc73c\ub85c \uad6c\ud560 \uc218 \uc788\ub2e4. \uc774\ub7ec\ud55c \uac1c\ub150\uc744 \uc77c\ubc18\ud654\ud558\uc5ec \ubbf8\ubd84\uc744 \uc815\uc758\ud560 \uc218 \uc788\ub2e4.<\/p>\n<p>\uc774 \ud3ec\uc2a4\ud2b8\uc5d0\uc11c\ub294 \uc2e4\uc22b\uac12 \ud568\uc218\uc758 \ubbf8\ubd84\uc744 \uc815\uc758\ud558\uace0 \uadf8 \uc131\uc9c8\uc744 \uc0b4\ud3b4\ubcf8\ub2e4.<\/p>\n<p><!-- #### #### #### #### #### #### #### #### #### #### #### #### #### --><\/p>\n<h3>\ubbf8\ubd84\uc758 \uc815\uc758<\/h3>\n<p>\ud568\uc218 \\(f\\)\uac00 \uc11c\ub85c \ub2e4\ub978 \ub450 \uc810 \\(a,\\) \\(b\\)\ub97c \uc6d0\uc18c\ub85c \uac16\ub294 \uad6c\uac04\uc5d0\uc11c \uc815\uc758\ub418\uc5b4 \uc788\ub2e4\uace0 \ud558\uc790. \uc774 \ub54c<br \/>\n\\[\\frac{f(b)-f(a)}{b-a}\\tag{1}\\]<br \/>\n\ub97c \\(x\\)\uac00 \\(a\\)\uc5d0\uc11c \\(b\\)\uae4c\uc9c0 \ubcc0\ud558\ub294 \ub3d9\uc548 \\(f\\)\uc758 <span class=\"defined\">\ud3c9\uade0\ubcc0\ud654\uc728<\/span>\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \uc774 \ud3c9\uade0\ubcc0\ud654\uc728\uc740 \ud568\uc218 \\(f\\)\uc758 \uadf8\ub798\ud504 \uc704\uc758 \ub450 \uc810 \\((a,\\,f(a)),\\) \\((b,\\,f(b))\\)\ub97c \uc9c0\ub098\ub294 \ud560\uc120\uc758 \uae30\uc6b8\uae30\uc640 \uac19\ub2e4.<\/p>\n<p>\ud568\uc218 \\(f\\)\uac00 \uc810 \\(x_0\\)\uc744 \uc6d0\uc18c\ub85c \uac16\ub294 \ud55c \uc5f4\ub9b0 \uad6c\uac04 \\(I\\)\uc5d0\uc11c \uc815\uc758\ub418\uc5b4 \uc788\uace0 \\(h \\ne 0\\)\uc774\uba70 \\(x_0 +h\\in I\\)\ub77c\uace0 \ud558\uc790. \uc774 \ub54c<br \/>\n\\[\\frac{f(x_0 +h)-f(x_0 )}{h}\\tag{2}\\]<br \/>\n\uc744 \uc810 \\(x_0\\)\uc5d0\uc11c \uc99d\ubd84 \\(h\\)\uc5d0 \ub300\ud55c \\(f\\)\uc758 <span class=\"defined\">\ucc28\ubd84\ubaab<\/span>\uc774\ub77c\uace0 \ubd80\ub978\ub2e4. \\(h\\)\uc758 \uac12\uc774 \\(0\\)\uc5d0 \uac00\uae4c\uc6b0\uba74 \uc774 \ucc28\ubd84\ubaab\uc740 \\(x_0\\) \uadfc\ucc98\uc5d0\uc11c \\(f\\)\uc758 \uac12\uc774 \uc5bc\ub9c8\ub098 \ube60\ub974\uac8c \ubcc0\ud654\ud558\ub294\uc9c0\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n<p>\ucc28\ubd84\ubaab \uc2dd (2)\uc5d0\uc11c \\(x_0\\)\uc744 \\(a\\)\ub85c \ubc14\uafb8\uace0 \\(h\\)\ub97c \\(b-a\\)\ub85c \ubc14\uafb8\uba74 \ud3c9\uade0\ubcc0\ud654\uc728 \uc2dd (1)\uc774 \ub41c\ub2e4. \uc774\ucc98\ub7fc \ud3c9\uade0\ubcc0\ud654\uc728\uacfc \ucc28\ubd84\ubaab\uc740 \ube44\uc2b7\ud55c \uc2dd\uc774\uc9c0\ub9cc, \ud3c9\uade0\ubcc0\ud654\uc728\uc740 \ub450 \uc810 \\(a,\\) \\(b\\) \ubaa8\ub450\uc5d0 \uad00\uc2ec\uc744 \uac16\ub294 \ubc18\uba74 \ucc28\ubd84\ubaab\uc740 \ud55c \uc810 \\(x_0\\)\uc5d0 \uad00\uc2ec\uc744 \uac00\uc9c4\ub2e4\ub294 \uc810\uc5d0\uc11c \uc4f0\uc784\uc0c8\uac00 \ub2e4\ub974\ub2e4.<\/p>\n<div class=\"definition\">\n<p><span class=\"definition\">\uc815\uc758 1. (\ubbf8\ubd84\uacc4\uc218)<\/span><\/p>\n<p>\ud568\uc218 \\(f\\)\uac00 \\(x_0\\)\uc744 \uc6d0\uc18c\ub85c \uac16\ub294 \ud55c \uc5f4\ub9b0 \uad6c\uac04\uc5d0\uc11c \uc815\uc758\ub418\uc5c8\ub2e4\uace0 \ud558\uc790. \ub9cc\uc57d \uadf9\ud55c<br \/>\n\\[\\lim_{h\\to 0}\\frac{f(x_0 +h) &#8211; f(x_0 )}{h}\\tag{3}\\]<br \/>\n\uc774 \uc874\uc7ac\ud558\uba74(\uc218\ub834\ud558\uba74), \uc774 \uadf9\ud55c\uac12\uc744 \\(x_0\\)\uc5d0\uc11c \\(f\\)\uc758 <span class=\"defined\">\ubbf8\ubd84\uacc4\uc218<\/span>(derivative)\ub77c\uace0 \ubd80\ub974\uace0 \\(f &#8216; (x_0 )\\)\uc73c\ub85c \ub098\ud0c0\ub0b8\ub2e4. \ub610\ud55c \uc810 \\(x_0\\)\uc5d0\uc11c \uc704 \uadf9\ud55c\uc774 \uc874\uc7ac\ud560 \ub54c \u2018\\(f\\)\ub294 \\(x_0\\)\uc5d0\uc11c <span class=\"defined\">\ubbf8\ubd84 \uac00\ub2a5<\/span>\ud558\ub2e4\u2019\ub77c\uace0 \ud45c\ud604\ud55c\ub2e4.\n<\/p>\n<\/div>\n<p>\ubbf8\ubd84\uacc4\uc218\uc758 \uc815\uc758\uc5d0\uc11c \uc2dd (3)\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc368\ub3c4 \ub41c\ub2e4.<br \/>\n\\[\\lim_{t\\to x_0}\\frac{f(x_0 ) &#8211; f(t)}{x_0 &#8211; t}\\]<br \/>\n\uc989 \ubbf8\ubd84\uacc4\uc218\ub294 \ucc28\ubd84\ubaab\uc758 \uadf9\ud55c\uc73c\ub85c \ud45c\ud604\ud560 \uc218\ub3c4 \uc788\uace0 \ud3c9\uade0\ubcc0\ud654\uc728\uc758 \uadf9\ud55c\uc73c\ub85c \ud45c\ud604\ud560 \uc218\ub3c4 \uc788\ub2e4.<\/p>\n<p>\ub2e4\ud56d\ud568\uc218\uc640 \uac19\uc774 \uac04\ub2e8\ud55c \ud568\uc218\ub294 \uc815\uc758\ub97c \uc774\uc6a9\ud558\uc5ec \ubbf8\ubd84\uacc4\uc218\ub97c \uc9c1\uc811 \uad6c\ud560 \uc218 \uc788\ub2e4.<\/p>\n<div class=\"example\">\n<p><span class=\"example\">\ubcf4\uae30 1.<\/span><br \/>\n\ud568\uc218 \\(f(x) = x^2\\)\uc5d0 \ub300\ud558\uc5ec \ubbf8\ubd84\uacc4\uc218 \\(f &#8216; (0) ,\\) \\(f &#8216; (1),\\) \\(f &#8216; (2)\\)\ub97c \uad6c\ud574 \ubcf4\uc790.<\/p>\n<p>\uc2dd (3)\uc5d0 \\(f(x) =x^2 ,\\) \\(x_0 =0\\)\uc744 \ub300\uc785\ud558\uba74<br \/>\n\\[\\lim_{h\\to 0} \\frac{f(0+h)-f(0)}{h} = \\lim_{h\\to 0} \\frac{(0+h)^2 &#8211; 0^2}{h}<br \/>\n= \\lim_{h\\to 0} \\frac{h^2}{h} = 0\\]<br \/>\n\uc73c\ub85c\uc11c \uadf9\ud55c\uac12\uc774 \uc874\uc7ac\ud558\ubbc0\ub85c \\(f\\)\ub294 \\(0\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\uace0 \\(f &#8216; (0) =0 \\)\uc774\ub2e4.<\/p>\n<p>\uac19\uc740 \ubc29\ubc95\uc73c\ub85c<br \/>\n\\[\\begin{align}<br \/>\nf &#8216; (1) &#038;= \\lim_{h\\to 0}\\frac{f(1+h)-f(1)}{h} = \\lim_{h\\to 0}\\frac{(1+h)^2 -1^2}{h} = \\lim_{h\\to 0}\\frac{2h + h^2}{h} =2 ,\\\\[6pt]<br \/>\nf &#8216; (2) &#038;= \\lim_{h\\to 0}\\frac{f(2+h)-f(2)}{h} = \\lim_{h\\to 0}\\frac{(2+h)^2 -2^2}{h} = \\lim_{h\\to 0}\\frac{4h + h^2}{h} =4<br \/>\n\\end{align}\\]<br \/>\n\uc774\ubbc0\ub85c \\(f\\)\ub294 \\(1,\\) \\(2\\)\uc5d0\uc11c \uac01\uac01 \ubbf8\ubd84 \uac00\ub2a5\ud558\uace0, \uc774 \ub450 \uc810\uc5d0\uc11c \ubbf8\ubd84\uacc4\uc218\ub294 \\(f &#8216; (1) = 2,\\) \\(f &#8216; (2) = 4\\)\uc774\ub2e4.\n<\/p>\n<\/div>\n<p>\ubcf4\uae30 1\uc5d0\uc11c \uc138 \ubbf8\ubd84\uacc4\uc218 \\(f &#8216; (0),\\) \\(f &#8216; (1),\\) \\(f &#8216; (2)\\)\uc758 \uac12\uc744 \uad6c\ud558\uc600\ub2e4. \ub9cc\uc57d \\(f\\)\uac00 \ubbf8\ubd84 \uac00\ub2a5\ud55c \uc810 \\(x\\)\uc5d0 \ub300\ud558\uc5ec \\(f &#8216; (x)\\)\ub97c \uc0dd\uac01\ud55c\ub2e4\uba74, \uc774 \uc2dd\uc740 \\(x\\)\ub97c \ubbf8\ubd84\uacc4\uc218 \\(f &#8216; (x)\\)\uc5d0 \ub300\uc751\uc2dc\ud0a4\ub294 \ud568\uc218\uac00 \ub41c\ub2e4. \uc774\ub7ec\ud55c \ud568\uc218\ub97c \\(f\\)\uc758 \ub3c4\ud568\uc218\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<div class=\"definition\">\n<p><span class=\"definition\">\uc815\uc758 2. (\ub3c4\ud568\uc218)<\/span><\/p>\n<p>\ud568\uc218 \\(f\\)\uac00 \ubbf8\ubd84 \uac00\ub2a5\ud55c \uc810\ub4e4\uc758 \uc9d1\ud569\uc744 \\(D\\)\ub77c\uace0 \ud558\uc790. \uc774 \ub54c \uac01 \uc810 \\(x \\in D\\)\ub97c \ubbf8\ubd84\uacc4\uc218 \\(f &#8216; (x)\\)\uc5d0 \ub300\uc751\uc2dc\ud0a4\ub294 \ud568\uc218<br \/>\n\\[f &#8216; : D \\,\\to\\, \\mathbb{R}\\]<br \/>\n\ub97c \\(f\\)\uc758 <span class=\"defined\">\ub3c4\ud568\uc218<\/span>\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n<\/div>\n<p>\\(f\\)\uc758 \ub3c4\ud568\uc218\ub97c \uad6c\ud558\ub294 \uac83\uc744 \u2018\\(f\\)\ub97c \ubbf8\ubd84\ud55c\ub2e4\u2019\ub77c\uace0 \ub9d0\ud55c\ub2e4. \uc989 \ub2e4\uc74c \ub450 \ud45c\ud604\uc740 \uac19\uc740 \uc758\ubbf8\uc774\ub2e4.<\/p>\n<ul>\n<li>\\(f\\)\uc758 \ub3c4\ud568\uc218\ub97c \uad6c\ud55c\ub2e4.<\/li>\n<li>\\(f\\)\ub97c \ubbf8\ubd84\ud55c\ub2e4.<\/li>\n<\/ul>\n<p>\ud568\uc218 \\(y=f(x)\\)\uc758 \ub3c4\ud568\uc218\ub97c \ub098\ud0c0\ub0b4\ub294 \uae30\ud638\ub294 \ubb34\ucc99 \ub2e4\uc591\ud55c\ub370, \uadf8 \uc911 \uc790\uc8fc \uc0ac\uc6a9\ub418\ub294 \uac83 \uba87 \uac1c\ub97c \ucd94\ub824\ubcf4\uba74 \ub2e4\uc74c\uacfc \uac19\ub2e4.<br \/>\n\\[<br \/>\nf &#8216; (x) ,\\,\\,\\,<br \/>\n\\frac{d}{dx}f(x) ,\\,\\,\\,<br \/>\n\\frac{df(x)}{dx} ,\\,\\,\\,<br \/>\n\\frac{df}{dx}(x) ,\\,\\,\\,<br \/>\n\\frac{dy}{dx} ,\\,\\,\\,<br \/>\n\\frac{d}{dx} y ,\\,\\,\\,<br \/>\nDf(x) ,\\,\\,\\,<br \/>\ny &#8216; ,\\,\\,\\,<br \/>\n\\dot{y} ,\\,\\,\\, \\cdots<br \/>\n\\]<br \/>\n\ub9cc\uc57d \ub3c4\ud568\uc218 \\(\\frac{dy}{dx}\\)\uc5d0 \\(x=x_0\\)\uc744 \ub300\uc785\ud55c \uc2dd(\ubbf8\ubd84\uacc4\uc218)\uc744 \ub098\ud0c0\ub0b4\uace0 \uc2f6\uc73c\uba74 \ub2e4\uc74c\uacfc \uac19\uc740 \uae30\ud638\ub97c \uc0ac\uc6a9\ud55c\ub2e4.<br \/>\n\\[\\left. \\frac{dy}{dx} \\right|_{x=x_0}\\]\n<\/p>\n<div class=\"example\">\n<p><span class=\"example\">\ubcf4\uae30 2.<\/span><br \/>\n\uc815\uc758\uc5ed\uc774 \\([0,\\, \\infty )\\)\uc778 \ud568\uc218 \\(g(x) = \\sqrt{x}\\)\uc758 \ub3c4\ud568\uc218\uc640 \ubbf8\ubd84\uacc4\uc218 \\(g &#8216; (4)\\)\ub97c \uad6c\ud574 \ubcf4\uc790.<\/p>\n<p>\\(x > 0\\)\uc77c \ub54c \\(g\\)\uc758 \ubbf8\ubd84\uacc4\uc218\ub294<br \/>\n\\[\\begin{align}<br \/>\ng &#8216; (x)<br \/>\n&#038;= \\lim_{h\\to 0}\\frac{g(x+h)-g(x)}{h} \\\\[6pt]<br \/>\n&#038;= \\lim_{h\\to 0}\\frac{\\sqrt{x+h} &#8211; \\sqrt{x}}{h} \\\\[6pt]<br \/>\n&#038;= \\lim_{h\\to 0}\\frac{(\\sqrt{x+h} &#8211; \\sqrt{x})(\\sqrt{x+h}+\\sqrt{x})}{h(\\sqrt{x+h}+\\sqrt{x})} \\\\[6pt]<br \/>\n&#038;= \\lim_{h\\to 0}\\frac{h}{h(\\sqrt{x+h}+\\sqrt{x})} \\\\[6pt]<br \/>\n&#038;= \\lim_{h\\to 0}\\frac{1}{\\sqrt{x+h}+\\sqrt{x}} \\\\[6pt]<br \/>\n&#038;= \\frac{1}{2\\sqrt{x}}<br \/>\n\\end{align}\\]<br \/>\n\uc774\ub2e4. \ud55c\ud3b8<br \/>\n\\[\\lim_{h\\to 0}\\frac{g(0+h)-g(0)}{h}<br \/>\n=\\lim_{h\\to 0^+}\\frac{\\sqrt{h}}{h}<br \/>\n=\\infty\\tag{4}\\]<br \/>\n\uc774\ubbc0\ub85c \\(g\\)\ub294 \\(0\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\uc9c0 \uc54a\ub2e4.<\/p>\n<p>\uadf8\ub7ec\ubbc0\ub85c \\(g\\)\uc758 \ub3c4\ud568\uc218 \\(g &#8216; \\)\uc758 \uc815\uc758\uc5ed\uc740 \ubaa8\ub4e0 \uc591\uc218\uc758 \uc9d1\ud569 \\(\\mathbb{R}^+\\)\uc774\uba70<br \/>\n\\[g &#8216; (x) = \\frac{1}{2\\sqrt{x}}\\]<br \/>\n\uc774\ub2e4. \ud55c\ud3b8 \\(4\\)\uc5d0\uc11c \\(g\\)\uc758 \ubbf8\ubd84\uacc4\uc218\ub294<br \/>\n\\[g &#8216; (4) = \\left. \\frac{1}{2\\sqrt{x}} \\right|_{x=4} = \\frac{1}{2\\sqrt{4}} = \\frac{1}{4}\\]<br \/>\n\uc774\ub2e4.\n<\/p>\n<\/div>\n<p>\uc704 \ubcf4\uae30\uc5d0\uc11c \ubcf4\ub2e4\uc2dc\ud53c \ub3c4\ud568\uc218\uc758 \uc815\uc758\uc5ed\uc740 \uc6d0\ub798 \ud568\uc218\uc758 \ubd80\ubd84\uc9d1\ud569\uc774\ub2e4. \uc989<br \/>\n\\[\\operatorname{dom} (f &#8216; ) \\subseteq \\operatorname{dom} (f)\\]<br \/>\n\uc774\ub2e4.<\/p>\n<p><!-- #### #### #### #### #### #### #### #### #### #### #### #### #### --><\/p>\n<h3>\uc88c\ubbf8\ubd84\uacc4\uc218\uc640 \uc6b0\ubbf8\ubd84\uacc4\uc218<\/h3>\n<p>\ubcf4\uae30 2\uc5d0\uc11c \\(g\\)\uc758 \uc815\uc758\uc5ed\uc774 \\([0,\\,\\infty )\\)\uc774\ubbc0\ub85c \\(0\\)\uc5d0\uc11c \\(g\\)\uc758 \ubbf8\ubd84\uacc4\uc218\ub97c \uad6c\ud558\uae30 \uc704\ud558\uc5ec \uc2dd (4)\uc640 \uac19\uc774 \\(0\\)\uc5d0\uc11c \uc6b0\uadf9\ud55c\uc744 \uacc4\uc0b0\ud558\uc600\ub2e4. \uc989 \uc815\uc758 1\uc5d0\uc11c\ub294 \uc810 \\(x_0\\)\uc5d0\uc11c \ud568\uc218 \\(f\\)\uc758 \ubbf8\ubd84\uacc4\uc218\ub97c \uc815\uc758\ud560 \ub54c\uc5d0\ub294 \\(f\\)\uac00 \\(x_0\\)\ub97c \uc6d0\uc18c\ub85c \uac16\ub294 \uc5f4\ub9b0 \uad6c\uac04\uc5d0\uc11c \uc815\uc758\ub41c\ub2e4\ub294 \uc870\uac74\uc744 \ub123\uc5c8\uc9c0\ub9cc, \uc774 \uc870\uac74\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \uc57d\ud654\ub420 \uc218 \uc788\ub2e4.<\/p>\n<div class=\"definition\">\n<p><span class=\"defined\">\uc815\uc758 3. (\uc88c\ubbf8\ubd84\uacc4\uc218\uc640 \uc6b0\ubbf8\ubd84\uacc4\uc218)<\/span><\/p>\n<p>\ud568\uc218 \\(f\\)\uac00 \uc810 \\(x_0\\)\uc744 \uc6d0\uc18c\ub85c \uac16\ub294 \uc9d1\ud569\uc5d0\uc11c \uc815\uc758\ub418\uc5c8\ub2e4\uace0 \ud558\uc790.<\/p>\n<ol class=\"bracket\">\n<li>\ub9cc\uc57d \uadf9\ud55c<br \/>\n\\[\\lim_{h\\to 0^-}\\frac{f(x_0 +h)-f(x_0 )}{h}\\]<br \/>\n\uc774 \uc874\uc7ac\ud558\uba74, \uc774 \uadf9\ud55c\uac12\uc744 \\(x_0\\)\uc5d0\uc11c \\(f\\)\uc758 <span class=\"defined\">\uc88c\ubbf8\ubd84\uacc4\uc218<\/span>\ub77c\uace0 \ubd80\ub974\uace0 \\(f_l &#8216; (x_0 )\\)\uc73c\ub85c \ub098\ud0c0\ub0b8\ub2e4.<\/li>\n<li>\ub9cc\uc57d \uadf9\ud55c<br \/>\n\\[\\lim_{h\\to 0^+}\\frac{f(x_0 +h)-f(x_0 )}{h}\\]<br \/>\n\uc774 \uc874\uc7ac\ud558\uba74, \uc774 \uadf9\ud55c\uac12\uc744 \\(x_0\\)\uc5d0\uc11c \\(f\\)\uc758 <span class=\"defined\">\uc6b0\ubbf8\ubd84\uacc4\uc218<\/span>\ub77c\uace0 \ubd80\ub974\uace0 \\(f_r &#8216; (x_0 )\\)\uc73c\ub85c \ub098\ud0c0\ub0b8\ub2e4.<\/li>\n<li>\ub9cc\uc57d \\(x_0\\)\uc774 \\(f\\)\uc758 \uc815\uc758\uc5ed\uc758 \uc67c\ucabd \ub05d\uc810\uc774\uba74 \\(x_0\\)\uc5d0\uc11c \\(f\\)\uc758 \ubbf8\ubd84\uacc4\uc218\ub294 \uc6b0\ubbf8\ubd84\uacc4\uc218\ub85c \uc815\uc758\ud55c\ub2e4. \ub9c8\ucc2c\uac00\uc9c0\ub85c \ub9cc\uc57d \\(x_0\\)\uc774 \\(f\\)\uc758 \uc815\uc758\uc5ed\uc758 \uc624\ub978\ucabd \ub05d\uc810\uc774\uba74 \\(x_0\\)\uc5d0\uc11c \\(f\\)\uc758 \ubbf8\ubd84\uacc4\uc218\ub294 \uc88c\ubbf8\ubd84\uacc4\uc218\ub85c \uc815\uc758\ud55c\ub2e4.<\/li>\n<\/ol>\n<\/div>\n<div class=\"remark\">\n<p><span class=\"remark\">\uc8fc\uc758.<\/span><br \/>\n\ud568\uc218\uc758 \uc88c\ubbf8\ubd84\uacc4\uc218\uc640 \ub3c4\ud568\uc218\uc758 \uc88c\uadf9\ud55c\uc740 \ub2e4\ub978 \uac1c\ub150\uc774\uba70, \ud568\uc218\uc758 \uc6b0\ubbf8\ubd84\uacc4\uc218\uc640 \ub3c4\ud568\uc218\uc758 \uc6b0\uadf9\ud55c\uc740 \ub2e4\ub978 \uac1c\ub150\uc774\ub2e4. \uc608\ucee8\ub300 \ud568\uc218 \\(f : \\mathbb{R} \\to \\mathbb{R}\\)\ub97c<br \/>\n\\[f(x) =<br \/>\n\\begin{cases}<br \/>\nx^2 \\sin \\frac{1}{x} &#038;\\quad \\text{if} \\,\\, x\\ne 0 \\\\[6pt]<br \/>\n0 &#038;\\quad \\text{if} \\,\\, x=0<br \/>\n\\end{cases}\\]<br \/>\n\uc774\ub77c\uace0 \ud558\uba74 \\(f\\)\ub294 \\(0\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\uace0 \\(0\\)\uc5d0\uc11c \\(f\\)\uc758 \ubbf8\ubd84\uacc4\uc218, \uc88c\ubbf8\ubd84\uacc4\uc218, \uc6b0\ubbf8\ubd84\uacc4\uc218 \ubaa8\ub450 \\(0\\)\uc774\ub2e4. \uc989<br \/>\n\\[f &#8216; (0) = f_l &#8216; (0) = f_r &#8216; (0) =0\\]<br \/>\n\uc774\ub2e4. \uadf8\ub7ec\ub098 \\(x \\ne 0\\)\uc77c \ub54c<br \/>\n\\[f &#8216; (x) = 2x \\sin \\frac{1}{x} &#8211; \\cos \\frac{1}{x}\\]<br \/>\n\uc774\ubbc0\ub85c \\(x\\to 0^+\\) \ub610\ub294 \\(x\\to 0^-\\)\uc77c \ub54c \\(f &#8216; (x)\\)\ub294 \uc218\ub834\ud558\uc9c0 \uc54a\ub294\ub2e4.<br \/>\n<span class=\"qee\"><\/span><\/p>\n<\/div>\n<div class=\"remark\">\n<p><span class=\"remark\">\ucc38\uace0.<\/span><br \/>\n\ucc45\uc5d0 \ub530\ub77c\uc11c\ub294 \u2018\ub2eb\ud78c \uad6c\uac04\uc5d0\uc11c\uc758 \ub3c4\ud568\uc218\u2019\ub97c \ub530\ub85c \uc815\uc758\ud558\uae30\ub3c4 \ud55c\ub2e4.<br \/>\n\uc989 \ud568\uc218 \\(f : D \\to \\mathbb{R}\\)\uc758 \uc815\uc758\uc5ed \\(D\\)\uac00 \uae38\uc774\uac00 \uc591\uc218\uc778 \ub2eb\ud78c \uad6c\uac04 \\([a,\\,b]\\)\ub97c \ud3ec\ud568\ud560 \ub54c \u2018\\([a,\\,b]\\)\uc5d0\uc11c \\(f\\)\uc758 \ub3c4\ud568\uc218\u2019\ub97c<br \/>\n\\[f &#8216; (x) = \\begin{cases}<br \/>\nf_r (a) &#038;\\quad\\text{if}\\,\\, x=a \\\\[8pt]<br \/>\nf(x) &#038;\\quad\\text{if}\\,\\,a < x < b \\\\[8pt]\nf_l (b) &#038;\\quad\\text{if}\\,\\, x=b\n\\end{cases}\\]\n\ub85c \uc815\uc758\ud558\uae30\ub3c4 \ud55c\ub2e4. \uc774\uc640 \uac19\uc774 \uc815\uc758\ud558\uba74 \\(a,\\) \\(b\\)\uc5d0\uc11c \\(f\\)\uac00 \ubbf8\ubd84 \ubd88\uac00\ub2a5\ud558\uc9c0\ub9cc \\([a,\\,b]\\)\uc5d0\uc11c \\(f\\)\uc758 \ub3c4\ud568\uc218\uac00 \uc874\uc7ac\ud558\ub294 \uacbd\uc6b0\uac00 \uc788\ub2e4. \uc608\ucee8\ub300 \ud568\uc218 \\(f : \\mathbb{R} \\to \\mathbb{R}\\)\ub97c\n\\[f(x) = \\begin{cases}\nx &#038;\\quad\\text{if}\\,\\, -3\\le x^2\\le 3 \\\\[8pt]\n0 &#038;\\quad\\text{otherwise}\n\\end{cases}\\]\n\uc73c\ub85c \uc815\uc758\ud558\uba74 \\(f\\)\ub294 \\(-3,\\) \\(3\\)\uc5d0\uc11c \ubbf8\ubd84 \ubd88\uac00\ub2a5\ud558\uc9c0\uba74 \\([-3,\\,3]\\)\uc5d0\uc11c \\(f\\)\uc758 \ub3c4\ud568\uc218\ub294 \\(f ' (x) = 2x\\)\uc774\ub2e4.\n<span class=\"qee\"><\/span><\/p>\n<\/div>\n<p><!-- #### #### #### #### #### #### #### #### #### #### #### #### #### --><\/p>\n<h3>\ubbf8\ubd84 \uac00\ub2a5\uc131\uacfc \uc5f0\uc18d\uc131\uc758 \uad00\uacc4<\/h3>\n<p>\uc9c1\uad00\uc801\uc73c\ub85c \ud568\uc218 \\(f\\)\uac00 \uc810 \\(x_0\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\ub2e4\ub294 \uac83\uc740 \\(x=x_0\\)\uc77c \ub54c \\(f\\)\uc758 \uadf8\ub798\ud504\uc758 \uc811\uc120\uc758 \uae30\uc6b8\uae30\ub97c \uad6c\ud560 \uc218 \uc788\ub2e4\ub294 \uac83\uc744 \uc758\ubbf8\ud558\ubbc0\ub85c, \\(f\\)\uc758 \uadf8\ub798\ud504\ub294 \uc810 \\((x_0 ,\\, f(x_0 ))\\)\uc5d0\uc11c \ub04a\uc5b4\uc9c0\uc9c0 \uc54a\uace0 \ub9e4\ub044\ub7fd\uac8c \uc774\uc5b4\uc838 \uc788\uc5b4\uc57c \ud55c\ub2e4. \uc774\uac83\uc744 \ub17c\ub9ac\uc801\uc73c\ub85c \uc99d\uba85\ud574 \ubcf4\uc790.<\/p>\n<div class=\"theorem\">\n<p><span class=\"theorem\">\uc815\ub9ac 1. (\ubbf8\ubd84 \uac00\ub2a5\uc131\uacfc \uc5f0\uc18d\uc131\uc758 \uad00\uacc4)<\/span><\/p>\n<p>\ud568\uc218 \\(f\\)\uac00 \uc810 \\(x_0\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\uba74 \\(f\\)\ub294 \\(x_0\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\ub2e4.<\/p>\n<\/div>\n<div class=\"proof\">\n<p class=\"proofname\">\uc99d\uba85<\/p>\n<p>\\(f\\)\uac00 \\(x_0\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\ubbc0\ub85c<br \/>\n\\[\\lim_{x\\to x_0}\\frac{f(x) &#8211; f(x_0)}{x-x_0} = f &#8216; (x_0 )\\]<br \/>\n\uc774\ub2e4. \ub530\ub77c\uc11c<br \/>\n\\[\\begin{align}<br \/>\n\\lim_{x\\to x_0} f(x)<br \/>\n&#038;= \\lim_{x\\to x_0} (f(x) &#8211; f(x_0 ) + f(x_0 )) \\\\[6pt]<br \/>\n&#038;= \\lim_{x\\to x_0} (f(x) &#8211; f(x_0)) + f(x_0) \\\\[4pt]<br \/>\n&#038;= \\lim_{x\\to x_0} \\frac{f(x) &#8211; f(x_0)}{x-x_0} (x-x_0 ) + f(x_0) \\\\[4pt]<br \/>\n&#038;= \\lim_{x\\to x_0} \\frac{f(x) &#8211; f(x_0)}{x-x_0} \\cdot \\lim_{x\\to x_0} (x-x_0 ) + f(x_0) \\\\[6pt]<br \/>\n&#038;= f &#8216; (x_0 ) \\cdot 0 + f(x_0) = f(x_0)<br \/>\n\\end{align}\\]<br \/>\n\uc774\ubbc0\ub85c \\(x_0\\)\uc5d0\uc11c \\(f\\)\uc758 \uadf9\ud55c\uac12\uacfc \ud568\uc22b\uac12\uc774 \uac19\ub2e4. \uc989 \\(f\\)\ub294 \\(x_0\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\ub2e4.<br \/>\n<span class=\"qed\"><\/span><\/p>\n<\/div>\n<div class=\"remark\">\n<p><span class=\"remark\">\uc8fc\uc758.<\/span> \uc815\ub9ac 1\uacfc \uad00\ub828\ud558\uc5ec \ub2e4\uc74c \uc0ac\uc2e4\uc5d0 \uc8fc\uc758\ud574\uc57c \ud55c\ub2e4.<\/p>\n<ol class=\"bracket\">\n<li>\uc815\ub9ac 1\uc758 \uc5ed\uc740 \uc131\ub9bd\ud558\uc9c0 \uc54a\ub294\ub2e4. \uc989 \\(f\\)\uac00 \\(x_0\\)\uc5d0\uc11c \uc5f0\uc18d\uc77c\uc9c0\ub77c\ub3c4 \\(f\\)\ub294 \\(x_0\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\uc9c0 \uc54a\uc744 \uc218 \uc788\ub2e4. \uc608\ucee8\ub300 \\(f(x) = \\lvert x \\rvert\\)\uc774\ub77c\uace0 \ud558\uba74 \\(f\\)\ub294 \\(0\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\uc9c0\ub9cc \\(0\\)\uc5d0\uc11c \ubbf8\ubd84 \ubd88\uac00\ub2a5\ud558\ub2e4. [\uc0ac\uc2e4 \\(\\mathbb{R}\\)\uc5d0\uc11c \uc5f0\uc18d\uc774\uc9c0\ub9cc \\(\\mathbb{R}\\)\uc758 \uc784\uc758\uc758 \uc810\uc5d0\uc11c \ubbf8\ubd84 \ubd88\uac00\ub2a5\ud55c \ud568\uc218\uac00 \uc874\uc7ac\ud55c\ub2e4. <a href=\"https:\/\/en.wikipedia.org\/wiki\/Weierstrass_function\">\ubc14\uc774\uc5b4\uc288\ud2b8\ub77c\uc2a4 \ud568\uc218(Weierstrass function)<\/a>\ub97c \ucc3e\uc544\ubcf4\ub77c.]<\/li>\n<li>\\(f\\)\uac00 \\(x_0\\)\uc744 \uc6d0\uc18c\ub85c \uac16\ub294 \uc5f4\ub9b0\uad6c\uac04\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud560\uc9c0\ub77c\ub3c4 \\(f &#8216; \\)\uc740 \\(x_0\\)\uc5d0\uc11c \uc5f0\uc18d\uc774 \uc544\ub2d0 \uc218 \uc788\ub2e4. \uc608\ucee8\ub300 \ud568\uc218 \\(f : \\mathbb{R} \\to \\mathbb{R}\\)\ub97c<br \/>\n\\[f(x) =<br \/>\n\\begin{cases}<br \/>\nx^2 \\sin \\frac{1}{x} &#038;\\quad \\text{if} \\,\\, x\\ne 0 \\\\[6pt]<br \/>\n0 &#038;\\quad \\text{if} \\,\\, x=0<br \/>\n\\end{cases}\\]<br \/>\n\uc774\ub77c\uace0 \uc815\uc758\ud558\uba74 \\(f\\)\ub294 \\(\\mathbb{R}\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud558\uc9c0\ub9cc \\(f &#8216; \\)\uc740 \\(0\\)\uc5d0\uc11c \ubd88\uc5f0\uc18d\uc774\ub2e4.<span class=\"qee\"><\/span><\/li>\n<\/ol>\n<\/div>\n<p><!-- #### #### #### #### #### #### #### #### #### #### #### #### #### --><\/p>\n<h3>\uace0\uacc4\ub3c4\ud568\uc218<\/h3>\n<p>\ud568\uc218 \\(f\\)\uac00 \ubbf8\ubd84 \uac00\ub2a5\ud558\uace0 \uadf8 \ub3c4\ud568\uc218 \\(f &#8216; \\)\ub3c4 \ubbf8\ubd84 \uac00\ub2a5\ud560 \ub54c \ub3c4\ud568\uc218\uc758 \ub3c4\ud568\uc218\ub97c \uad6c\ud560 \uc218 \uc788\ub294\ub370 \uc774 \ud568\uc218\ub97c <span class=\"defined\">\uc774\uacc4\ub3c4\ud568\uc218<\/span>\ub77c\uace0 \ubd80\ub978\ub2e4. \uc989 \ud568\uc218 \\(f\\)\uac00 \ub450 \ubc88 \ubbf8\ubd84 \uac00\ub2a5\ud55c \uc810\ub4e4\uc758 \uc9d1\ud569\uc744 \\(D\\)\ub77c\uace0 \ud560 \ub54c, \\(f\\)\uc758 \uc774\uacc4\ub3c4\ud568\uc218\ub294 \uc784\uc758\uc758 \\(x\\in D\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[f &#8216; &#8216; (x) = \\frac{d}{dx} f &#8216; (x)\\]<br \/>\n\ub85c \uc815\uc758\ub41c \ud568\uc218\uc774\ub2e4. \ud568\uc218 \\(y=f(x)\\)\uc758 \uc774\uacc4\ub3c4\ud568\uc218\ub97c \ub098\ud0c0\ub0b4\ub294 \uae30\ud638\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \uac83\ub4e4\uc774 \uc788\ub2e4.<br \/>\n\\[f &#8216; &#8216; (x) ,\\,\\,\\,<br \/>\n\\frac{d^2}{dx^2} f(x) ,\\,\\,\\,<br \/>\n\\frac{d^2 f(x)}{dx^2} ,\\,\\,\\,<br \/>\n\\frac{d^2 f}{dx^2} (x) ,\\,\\,\\,<br \/>\n\\frac{d^2 y}{dx^2} ,\\,\\,\\,<br \/>\n\\frac{d^2}{dx^2} y ,\\,\\,\\,<br \/>\nD^2 f(x) ,\\,\\,\\,<br \/>\ny &#8216; &#8216; ,\\,\\,\\,<br \/>\n\\ddot{y} ,\\,\\,\\,<br \/>\n\\cdots\\]<br \/>\n\ube44\uc2b7\ud558\uac8c, \\(n\\)\uc774 \\(2\\) \uc774\uc0c1\uc778 \uc790\uc5f0\uc218\uc774\uace0 \\(f\\)\uac00 \\(n\\)\ubc88 \ubbf8\ubd84 \uac00\ub2a5\ud55c \uc810\ub4e4\uc758 \uc9d1\ud569\uc744 \\(D\\)\ub77c\uace0 \ud560 \ub54c, \\(f\\)\uc758 <span class=\"defined\">\\(n\\)\uacc4\ub3c4\ud568\uc218<\/span>\ub294 \uc784\uc758\uc758 \\(x\\in D\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[f^{(n)} (x) = \\frac{d}{dx} f^{(n-1)}(x)\\]<br \/>\n\ub85c \uc815\uc758\ub41c \ud568\uc218\uc774\ub2e4. \ud568\uc218 \\(y=f(x)\\)\uc758 \\(n\\)\uacc4\ub3c4\ud568\uc218\ub97c \ub098\ud0c0\ub0b4\ub294 \uae30\ud638\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \uac83\ub4e4\uc774 \uc788\ub2e4.<br \/>\n\\[f^{(n)} (x) ,\\,\\,\\,<br \/>\n\\frac{d^n}{dx^n} f(x) ,\\,\\,\\,<br \/>\n\\frac{d^n f(x)}{dx^n} ,\\,\\,\\,<br \/>\n\\frac{d^n f}{dx^n} (x) ,\\,\\,\\,<br \/>\n\\frac{d^n y}{dx^n} ,\\,\\,\\,<br \/>\n\\frac{d^n}{dx^n} y ,\\,\\,\\,<br \/>\nD^n f(x) ,\\,\\,\\,<br \/>\ny^{(n)} ,\\,\\,\\,<br \/>\n\\cdots\\]<br \/>\n\\(I\\)\uac00 \\(\\mathbb{R}\\)\uc758 \ubd80\ubd84\uc9d1\ud569\uc774\uace0 \\(n\\)\uc774 \uc790\uc5f0\uc218\ub77c\uace0 \ud558\uc790. \\(I\\)\uc758 \ubaa8\ub4e0 \uc810\uc5d0\uc11c \\(n\\)\ubc88 \ubbf8\ubd84 \uac00\ub2a5\ud55c \ud568\uc218\ub4e4\uc758 \ubaa8\uc784\uc744 \\(D^n (I)\\)\ub85c \ub098\ud0c0\ub0b4\uba70, \ud2b9\ud788 \\(I\\)\uc5d0\uc11c \ubbf8\ubd84 \uac00\ub2a5\ud55c \ud568\uc218\ub4e4\uc758 \ubaa8\uc784 \\(D^1 (I)\\)\ub97c \uac04\ub2e8\ud788 \\(D(I)\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4. \ub610\ud55c \\(D^n (I)\\)\uc5d0 \uc18d\ud558\ub294 \ud568\uc218 \uc911\uc5d0\uc11c \\(n\\)\uacc4\ub3c4\ud568\uc218\uac00 \uc5f0\uc18d\uc778 \ud568\uc218\ub4e4\uc758 \ubaa8\uc784\uc744 \\(C^n (I)\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4. \ud2b9\ud788 \\(C^0 (I)\\)\ub294 \\(I\\)\uc5d0\uc11c \uc5f0\uc18d\uc778 \ud568\uc218\ub4e4\uc758 \ubaa8\uc784\uc744 \ub098\ud0c0\ub0b4\uba70, \uac04\ub2e8\ud788 \\(C (I)\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\n<p>\\(f\\in C^1 (I)\\)\uc77c \ub54c \u2018\\(f\\)\ub294 \\(I\\)\uc5d0\uc11c \uc5f0\uc18d\uc778 \ub3c4\ud568\uc218\ub97c \uac00\uc9c4\ub2e4\u2019 \ub610\ub294 \u2018\\(f\\)\ub294 \\(I\\)\uc5d0\uc11c <span class=\"defined\">\ub9e4\ub044\ub7ec\uc6b4 \ud568\uc218<\/span>(smooth function)\uc774\ub2e4\u2019 \ub610\ub294 \u2018\\(f\\)\ub294 \\(C^1\\)\uae09\uc774\ub2e4\u2019\ub77c\uace0 \ud45c\ud604\ud55c\ub2e4. \ub610\ud55c \\(f\\in C^n (I)\\)\uc77c \ub54c \u2018\\(f\\)\ub294 \\(I\\)\uc5d0\uc11c \uc5f0\uc18d\uc778 \\(n\\)\uacc4\ub3c4\ud568\uc218\ub97c \uac00\uc9c4\ub2e4\u2019 \ub610\ub294 \u2018\\(f\\)\ub294 \\(C^n\\)\uae09\uc774\ub2e4\u2019\ub77c\uace0 \ud45c\ud604\ud55c\ub2e4. \ucc45\uc5d0 \ub530\ub77c\uc11c\ub294 \\(f\\in C^1 (I)\\)\uc778 \uac83\uc744 \u2018\\(f\\)\ub294 \\(I\\)\uc5d0\uc11c <span class=\"defined\">\uc5f0\uc18d\uc801\uc73c\ub85c \ubbf8\ubd84 \uac00\ub2a5\ud558\ub2e4<\/span>(continuously differentiable)\u2019\ub77c\uace0 \ud45c\ud604\ud558\uae30\ub3c4 \ud55c\ub2e4.<\/p>\n<p>\uc815\uc758\uc5d0 \uc758\ud558\uba74<br \/>\n\\[C(I) \\subsetneq D(I) \\subsetneq C^1 (I) \\subsetneq D^2 (I) \\subsetneq C^2 (I) \\subsetneq D^3 (I) \\subsetneq C^3 (I) \\subsetneq \\cdots<br \/>\n\\]<br \/>\n\uc774\ub2e4. \ud55c\ud3b8 \\(I\\)\uc5d0\uc11c \uc784\uc758 \ud69f\uc218\ub85c \ubbf8\ubd84 \uac00\ub2a5\ud55c \ud568\uc218\ub4e4\uc758 \ubaa8\uc784\uc744 \\(C^{\\infty} (I)\\) \ub610\ub294 \\(D^{\\infty} (I)\\)\ub85c \ub098\ud0c0\ub0b8\ub2e4. \uc815\uc758\uc5d0 \uc758\ud558\uba74 \uc784\uc758\uc758 \uc790\uc5f0\uc218 \\(n\\)\uc5d0 \ub300\ud558\uc5ec<br \/>\n\\[D^n (I) \\subsetneq C^n (I) \\subsetneq D^{\\infty} (I) = C^{\\infty} (I)\\]<br \/>\n\uc774\ub2e4. (\ucc38\uace0\ub85c \\(I\\)\uc5d0\uc11c \uc784\uc758 \ud69f\uc218\ub85c \ubbf8\ubd84 \uac00\ub2a5\ud55c \ud568\uc218\ub4e4\uc758 \ubaa8\uc784\uc744 \ub098\ud0c0\ub0bc \ub54c \\(D^{\\infty}(I)\\)\ubcf4\ub2e4 \\(C^{\\infty}(I)\\)\ub97c \ub354 \ub9ce\uc774 \uc0ac\uc6a9\ud55c\ub2e4.)<\/p>\n<div class=\"example\">\n<p><span class=\"example\">\uc608\uc81c 3.<\/span><br \/>\n\ub3db\uc774 \uc5c6\ub294 \uc720\uc120\ud615 \ubc30\uc5d0 \ub3db\uc744 \ub2e4\ub294 \uc218\ud559\uc801\uc778 \ubc29\ubc95\uc744 \uad6c\ud558\uc2dc\uc624.<\/p>\n<p><span class=\"proof\">\uc815\ub2f5.<\/span> \u201c\ubbf8\ubd84\ud55c\ub2e4.\u201d<\/p>\n<p><span class=\"proof\">\ud480\uc774.<\/span> \uc8fc\uc5b4\uc9c4 \ubc30\ub97c \\(s\\)\ub77c\uace0 \ud558\uc790. \uadf8\ub7ec\uba74 \\(s\\)\ub294 \uc720\uc120\ud615\uc774\ubbc0\ub85c \ub9e4\ub044\ub7fd\ub2e4. \ub530\ub77c\uc11c \\(s\\)\ub294 \ubbf8\ubd84 \uac00\ub2a5\ud558\ub2e4. \\(s\\)\ub97c \ubbf8\ubd84\ud558\uba74 \\(\\dot{s}\\)\ub85c\uc11c \\(s\\)\uc5d0 \ub3db(dot)\uc774 \ub2ec\ub9b0\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \uc815\ub2f5\uc740 \u201c\ubbf8\ubd84\ud55c\ub2e4\u201d\uc774\ub2e4.<br \/>\n<span class=\"qee\"><\/span><\/p>\n<\/div>\n<div class=\"example\">\n<p><span class=\"example\">\uc608\uc81c 4.<\/span><br \/>\n\uad6c\ud615 \ud734\ub300\uc804\ud654 \u2018\uc635\ud2f0\uba38\uc2a4\u2019\ub97c \uc0b4\uc544 \uc6c0\uc9c1\uc774\uac8c \ub9cc\ub4dc\ub294 \uc218\ud559\uc801\uc778 \ubc29\ubc95\uc744 \uad6c\ud558\uc2dc\uc624.<\/p>\n<p><span class=\"proof\">\uc815\ub2f5.<\/span> \u201c\ubbf8\ubd84\ud55c\ub2e4.\u201d<\/p>\n<p><span class=\"proof\">\ud480\uc774.<\/span> \u2018\uc635\ud2f0\uba38\uc2a4\u2019\ub97c \ubbf8\ubd84\ud558\uba74 \u2018\uc635\ud2f0\uba38\uc2a4 \ud504\ub77c\uc784\u2019\uc774 \ub418\uc5b4 \uc0b4\uc544 \uc6c0\uc9c1\uc774\uac8c \ub41c\ub2e4. (\ub2e8, \uc6b0\uc8fc\ub85c \ub0a0\uc544\uac08 \uc218\ub3c4 \uc788\uc73c\ub2c8 \uc8fc\uc758\ud560 \uac83.)<br \/>\n<span class=\"qee\"><\/span><\/p>\n<\/div>\n<h3><\/h3>\n<h3><\/h3>\n","protected":false},"excerpt":{"rendered":"<p>\ud568\uc218 \\(y=f(x)\\)\uc758 \uadf8\ub798\ud504\uac00 \ubfb0\uc871\ud55c \ubd80\ubd84\uc774 \uc5c6\uace0 \ub9e4\ub044\ub7fd\uac8c \uc774\uc5b4\uc838 \uc788\uc744 \ub54c \uadf8\ub798\ud504 \uc704\uc758 \ud55c \uc810\uc5d0\uc11c \uc811\uc120\uc744 \uc0dd\uac01\ud560 \uc218 \uc788\ub2e4. \uc774 \uc811\uc120\uc758 \uae30\uc6b8\uae30\ub294 \uc811\uc810 \uadfc\ucc98\uc5d0\uc11c \\(x\\)\uc758 \ubcc0\ud654\ub7c9\uacfc \\(y\\)\uc758 \ubcc0\ud654\ub7c9\uc758 \ube44\uc758 \uadf9\ud55c\uac12\uc73c\ub85c \uad6c\ud560 \uc218 \uc788\ub2e4. \uc774\ub7ec\ud55c \uac1c\ub150\uc744 \uc77c\ubc18\ud654\ud558\uc5ec \ubbf8\ubd84\uc744 \uc815\uc758\ud560 \uc218 \uc788\ub2e4. \uc774 \ud3ec\uc2a4\ud2b8\uc5d0\uc11c\ub294 \uc2e4\uc22b\uac12 \ud568\uc218\uc758 \ubbf8\ubd84\uc744 \uc815\uc758\ud558\uace0 \uadf8 \uc131\uc9c8\uc744 \uc0b4\ud3b4\ubcf8\ub2e4. \ubbf8\ubd84\uc758 \uc815\uc758 \ud568\uc218 \\(f\\)\uac00 \uc11c\ub85c \ub2e4\ub978 \ub450 \uc810 \\(a,\\) \\(b\\)\ub97c \uc6d0\uc18c\ub85c \uac16\ub294 \uad6c\uac04\uc5d0\uc11c \uc815\uc758\ub418\uc5b4 \uc788\ub2e4\uace0 \ud558\uc790.&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"categories":[47],"tags":[197,84,189,194,190,195,185,188,196,192,193,191,187,186],"class_list":["post-1938","post","type-post","status-publish","format-standard","hentry","category-calculus-ap","tag-continuously-differentiable","tag-derivative","tag-differentiation","tag-194","tag-190","tag-195","tag-185","tag-188","tag-196","tag-192","tag-193","tag-191","tag-187","tag-186"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/1938","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=1938"}],"version-history":[{"count":66,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/1938\/revisions"}],"predecessor-version":[{"id":2783,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/1938\/revisions\/2783"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=1938"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/categories?post=1938"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/tags?post=1938"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}