{"id":2012,"date":"2019-10-12T22:26:32","date_gmt":"2019-10-12T13:26:32","guid":{"rendered":"http:\/\/141.164.34.82\/?p=2012"},"modified":"2019-10-12T22:31:32","modified_gmt":"2019-10-12T13:31:32","slug":"%eb%8f%84%eb%8c%80%ec%b2%b4-%ea%b7%b8%eb%9e%98%eb%94%94%ec%96%b8%ed%8a%b8%ea%b0%80-%eb%ac%b4%ec%97%87%ec%9d%b8%ea%b0%80","status":"publish","type":"post","link":"http:\/\/ds.sumeun.org\/?p=2012","title":{"rendered":"\ub3c4\ub300\uccb4 \uadf8\ub798\ub514\uc5b8\ud2b8\uac00 \ubb34\uc5c7\uc778\uac00?"},"content":{"rendered":"<h2>\uc9c8\ubb38: \uadf8\ub798\ub514\uc5b8\ud2b8\ub780 \ubb34\uc5c7\uc778\uac00?[<sup>1]<\/sup><\/h2>\n<p>[<sup>1]:<\/sup> \uc774 \uae00\uc758 \uc77c\ubd80\ub294 \ucd9c\uac04 \uc608\uc815\uc778 <strong>&lt;\uc218\ud559\uc758 \uc228\uc740 \uc6d0\ub9ac 2&gt;<\/strong>\uc758 \uc6d0\uace0 \uc77c\ubd80\ub97c \ubc1c\ucdcc\ud55c \uac83\uc785\ub2c8\ub2e4.<\/p>\n<p>\uc77c\uc804\uc5d0 facebook\uc5d0\uc11c \uadf8\ub798\ub514\uc5b8\ud2b8\uac00 \ubb34\uc5c7\uc778\uc9c0\uc5d0 \ub300\ud574 \ud55c\ucc3d \ub17c\ub780\uc774 \uc788\uc5c8\ub2e4. \uc5b4\ub5a4 \uc0ac\ub78c\ub4e4\uc740 \uadf8\ub798\ub514\uc5b8\ud2b8\uac00 <strong>\uae30\uc6b8\uae30<\/strong>\ub77c\uace0 \ud558\uace0, \uc5b4\ub5a4 \uc0ac\ub78c\uc740 \ub2e8\uc21c\ud788 <strong>\ubc29\ud5a5<\/strong>\uc774\ub77c\uace0 \ud588\ub2e4. \uadf8\ub9ac\uace4 \ub2e4\ub978 \uc0ac\ub78c\uc774 \uacf5\uc2dd \ud558\ub098\ub97c \ubcf4\uc5ec\uc8fc\ub294 \uac83\uc73c\ub85c \ud6c8\ud6c8\ud788(?) \ub9c8\ubb34\ub9ac\uac00 \ub418\uc5c8\ub2e4. (\uadf8\ub807\uc9c0! \uc218\ud559\uc774\ub780 \ubaa8\ub984\uc9c0\uae30 \uacf5\uc2dd\uc73c\ub85c \ub9d0\ud558\ub294 \uac83\uc774\ub2e4!?)<\/p>\n<p>\uadf8\ub7f0\ub370 \uc815\ub9d0\ub85c, \uadf8\ub798\ub514\uc5b8\ud2b8\uac00 \ubb34\uc5c7\uc778\uac00?<\/p>\n<h3>\uc218\ud559\uc740 \uae30\ud638\uc77c \ubfd0\uc774\uc9c0\ub9cc, \uc0c1\uc0c1\ud560 \uc218 \uc788\ub2e4\uba74 \uc27d\ub2e4.<\/h3>\n<p>\uc0ac\uc2e4 \uc218\ud559\uc790\ub4e4\uc774 \uc5c4\ubc00\ud558\uac8c \uc0dd\uac01\ud558\ub294 \uc218\ud559\uc774\ub780, \uc544\ub2c8 \uc801\uc5b4\ub3c4 \uc99d\uba85\uc744 \ud560\ub54c\uc5d0\ub294, \ub2e8\uc21c\ud788 \uae30\ud638\uc758 \ub098\uc5f4\uc774\ub77c\uc11c \uadf8\uac78 \uc5b4\ub5bb\uac8c \uc0dd\uac01\ud574 \ub0c8\uac74, \uc5b4\ub5bb\uac8c \uc0c1\uc0c1\ud574 \ud574\ub0c8\uac74 \uc0c1\uad00 \uc5c6\ub2e4(\uc8fc\uc5b4\uc9c4 \uacf5\ub9ac\uc640 \ud0c0\ub2f9\ud55c \uc5f0\uc5ed \uaddc\uce59\uc744 \uc0ac\uc6a9\ud558\uae30\ub9cc \ud558\uba74 \ub41c\ub2e4).<\/p>\n<p>\uc608\ub97c \ub4e4\uc5b4 1+1=2\uc774\uace0, \uc774\uac78 \uc810 2\uac1c\ub85c \uc0c1\uc0c1\ud558\uac74, \uc544\uc774\uc2a4\ud06c\ub9bc 2\uac1c\ub85c \uc0dd\uac01\ud558\uac74 \ubb38\uc81c\uac00 \uc5c6\ub2e4. \uc0ac\uc2e4 \uc810 2\uac1c, \uc544\uc774\uc2a4\ud06c\ub9bc 2\uac1c, \uc0ac\ud0d5 2\uac1c, \ub9c9\ub300 2\uac1c\uc5d0\uc11c \uc218 2\ub97c \ucd94\ucd9c\ud574\ub0b4\ub294 \uac83\ub3c4 \uad49\uc7a5\ud55c \ucd94\uc0c1\ud654, \uc77c\ubc18\ud654 \uacfc\uc815\uc774 \ud544\uc694\ud558\ub2e4. \uadf8\ub798\uc11c \uc5c4\ubc00\ud558\uac8c \ub9d0\ud574, 1+1=2\uc640 \uc544\uc774\uc2a4\ud06c\ub9bc 1\uac1c\uc640 \uc544\uc774\uc2a4\ud06c\ub9bc 1\uac1c\ub97c \ud569\uce58\uba74 \uc544\uc774\uc2a4\ud06c\ub9bc\uc774 2\uac1c\ub77c\ub294 \uba85\uc81c\ub294 a-a=0\uacfc 3-3=0\ub9cc\ud07c\uc774\ub098 \ud070 \uac04\uadf9\uc774 \uc788\ub2e4(\ub77c\uace0 \uc0dd\uac01\ud558\uc9c0\ub9cc,). \uacc4\uc0b0\uc744 \ube68\ub9ac\ud558\uae30 \uc704\ud574 \uc8fc\ud310\uc744 \uc190\uac00\ub77d\uc73c\ub85c \uc624\ub974\ub77d \ub0b4\ub9ac\ub77d\ud55c\ub2e4\uace0 \uafb8\uc911\ud560 \uc0ac\ub78c\ub3c4 \uc5c6\ub2e4(\ubb3c\ub860 \uc8fc\ud310\uc744 \uc0ac\uc6a9\ud558\ub294 \ub300\ubd80\ubd84\uc758 \uacbd\uc6b0\ub294 \uc2e4\uc81c \uc0ac\ubb3c\uc774\ub098 \ub3c8\uc744 \ub300\uc0c1\uc73c\ub85c \ud558\ub294 \uac83\uc774\uaca0\uc9c0\ub9cc).<\/p>\n<h3>\ub300\uc218\uc640 \uae30\ud558<\/h3>\n<p>\uadf8\ub7fc\uc5d0\ub3c4 \ubd88\uad6c\ud558\uace0 \ub370\uce74\ub974\ud2b8\ub294 <strong>\uae30\ud558\uc758 \ub300\uc218\ud654<\/strong>\uc5d0 \uc131\uacf5\ud588\uc73c\uba70, \uc6b0\ub9ac\ub294 \\(2x+2y=0\\) \ub97c 2\ucc28\uc6d0 \ud3c9\uba74 \uc704\uc758 \uc9c1\uc120\uc744 \ub098\ud0c0\ub0b8\ub2e4\uace0 \uc0dd\uac01\ud560 \uc218 \uc788\ub2e4. \uadf8\ub9ac\uace0 \ub300\uc218\ud654\ub41c \uae30\ud558\uc758 \uc911\uc694\uc131\uc740 4\ucc28\uc6d0, 5\ucc28\uc6d0\ucc98\ub7fc \ub208\uc73c\ub85c \ubcfc \uc218\ub3c4 \uc5c6\uace0, \uc9c1\uad00\uc801\uc73c\ub85c \uc0c1\uc0c1\ud560 \uc218\ub3c4 \uc5c6\ub294 \ub300\uc0c1\uc744 \ud0d0\uad6c\ud560 \ub54c \ub4dc\ub7ec\ub09c\ub2e4.<\/p>\n<h2>\uadf8\ub798\uc11c \uadf8\ub798\ub514\uc5b8\ud2b8\ub780 \ubb34\uc5c7\uc778\uac00?<\/h2>\n<p>\uadf8\ub798\ub514\uc5b8\ud2b8\ub294 1\ubcc0\uc218 \ud568\uc218 \uadf8\ub798\ud504\uc5d0\uc11c \uae30\uc6b8\uae30\uc640 \ube44\uc2b7\ud55c \uc5ed\ud560\uc744 \ud558\ub294\ub370, \uae30\uc6b8\uae30\ub77c\uace0 \ub9d0\ud558\uae34 \ud798\ub4e4\ub2e4. \uc65c\ub0d0\ud558\uba74 \uc704\uc5d0\uc11c \uc598\uae30\ud55c \ud1a0\ub860\uc5d0\uc11c\ub3c4 \uc9c0\uc801\ub418\uc5c8\ub4ef\uc774 \uc5ec\ub7ec \uac12\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 <strong>\ubca1\ud130<\/strong>\uc774\uae30 \ub54c\ubb38\uc774\ub2e4. \ubca1\ud130\ub294 \ud754\ud788 <strong>\ubc29\ud5a5<\/strong>\uacfc <strong>\ud06c\uae30<\/strong>\ub97c \ub3d9\uc2dc\uc5d0 \ub098\ud0c0\ub0b8\ub2e4\uace0 \ub9d0\ud55c\ub2e4.<\/p>\n<p>\uadf8\ub798\uc11c \ub2e4\ub978 \uc0ac\ub78c\uc740 \uadf8\ub798\ub514\uc5b8\ud2b8\ub294 \uae30\uc6b8\uae30\uac00 \uc544\ub2c8\ub77c \uc21c\uac04\ubcc0\ud654\uc728\uc774 \uac00\uc7a5 \ud070 \ubc29\ud5a5\uc744 \ub098\ud0c0\ub0b8\ub2e4\uace0 \uc8fc\uc7a5\ud588\ub2e4. \uc77c\ub9ac\uac00 \uc788\ub294 \ub9d0\uc774\ub2e4. \uadf8\ub798\ub514\uc5b8\ud2b8 \ub514\uc13c\ud2b8\uc5d0\uc11c\ub3c4 \uadf8\ub798\ub514\uc5b8\ud2b8\ub97c \uc4f0\ub294 \uc774\uc720\ub294 \ud568\uc218\uac12\uc744 \ucd5c\ub300\ud55c \ube60\ub974\uac8c \uac10\uc18c\uc2dc\ud0a4\uae30 \uc704\ud574\uc11c\uc774\ub2e4. \ud568\uc218\uac12\uc744 \ubcc0\ud654\uc2dc\ud0a4\ub824\uba74 \uc785\ub825\uac12\uc744 \ubcc0\ud654\uc2dc\ucf1c\uc57c \ud558\uace0, \uc785\ub825\uac12\uc744 \uc5b4\ub5a4 \uc2dd\uc73c\ub85c \ubcc0\ud654\uc2dc\ucf1c\uc57c \ud568\uc218\uac12\uc744 \uac00\uc7a5 \ube60\ub974\uac8c \ucd5c\uc18c\ud654\ud560 \uc218 \uc788\ub294\uc9c0\ub97c \uadf8\ub798\ub514\uc5b8\ud2b8\uac00 \uc54c\ub824\uc8fc\ub294 \uac83\uc774\ub2e4. \ud558\uc9c0\ub9cc \uadf8\ub798\ub514\uc5b8\ud2b8\ub77c\ub294 \ubca1\ud130 \ud568\uc218\ub294 \uc785\ub825\uac12\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c \ubca1\ud130\ub97c \ucd9c\ub825\ud55c\ub2e4. \uc55e\uc5d0\uc11c \uc598\uae30\ud588\ub4ef\uc774 \ubca1\ud130\ub294 \ubc29\ud5a5\uacfc \ud06c\uae30\ub97c \ub3d9\uc2dc\uc5d0 \uac00\uc9c0\uace0 \uc788\uae30 \ub54c\ubb38\uc5d0 \ub2e8\uc21c\ud788 \uc21c\uac04\ubcc0\ud654\uc728\uc774 \uac00\uc7a5 \ud070 \ubc29\ud5a5\uc774\ub77c\uace0 \ud558\uae30\uc5d0\ub294 \ubb54\uac00 \ubd80\uc871\ud558\ub2e4. <\/p>\n<h3>\ub300\uc218\ud559(Algebra)\uc774\ub780?<\/h3>\n<p>\uc22b\uc790 2\uac00 \ub3cc 2\uac1c, \uc790\ub3d9\ucc28 2\uac1c, \ubc14\ub098\ub098 2\uac1c\uc758 \ucd94\uc0c1\ud654\/\uc77c\ubc18\ud654\ub77c\uba74, \ub300\uc218\ud559\uc758 \ubcc0\uc218 \\(x\\) \ub294 \uc22b\uc790 \\(1,2,3\\) \ub4f1\uc758 \ucd94\uc0c1\ud654\/\uc77c\ubc18\ud654\ub77c\uace0 \uc0dd\uac01\ud560 \uc218 \uc788\ub2e4. <\/p>\n<p>\ub300\uc218\ud559\uc5d0\uc11c\uc758 \uad00\uc2ec\uc740 \ubcc0\uc218\uac00 \ud3ec\ud568\ub41c \ub4f1\uc2dd, \ubd80\ub4f1\uc2dd \ub4f1\uc774\uace0, \uc774\ub4e4 \ub4f1\uc2dd, \ubd80\ub4f1\uc2dd\uc740 \uc77c\uc815\ud55c \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub294 <strong>\ubaa8\ub4e0 \uad6c\uccb4\uc801\uc778 \uc218<\/strong>\uc5d0 \ub300\ud574 \uc131\ub9bd\ud55c\ub2e4. \uc608\ub97c \ub4e4\uc5b4 \uc720\uba85\ud55c \uc0b0\uc220\ud3c9\uade0\uacfc \uae30\ud558\ud3c9\uade0\uc758 \uad00\uacc4\ub294 0\ubcf4\ub2e4 \ud070 \ubaa8\ub4e0 \uc2e4\uc218\uc5d0 \ub300\ud574 \uc131\ub9bd\ud558\uace0, \uadf8\uac83\uc744 \uc99d\uba85\ud560 \uc218 \uc788\ub2e4!<\/p>\n<p>\\[\\frac{a+b}{2} \\geq \\sqrt{ab} \\ \\ (a \\geq 0, b \\geq 0)\\]<\/p>\n<p>\uc6b0\uc640! \uc2e0\uae30\ud558\ub2e4. \uc5b4\ub5bb\uac8c <strong>\ubaa8\ub4e0 \uc591\uc218<\/strong>\uc5d0 \ub300\ud574 \uc704\uc758 \ub4f1\uc2dd \uc131\ub9bd\ud55c\ub2e4\ub294 \uac83\uc744 \uc54c\uc558\ub370?<\/p>\n<p>\uc0ac\uc2e4 \ub300\uc218\ud559\uc774 \uae30\ud638\ub97c \uc0ac\uc6a9\ud558\uae30 \ub54c\ubb38\uc5d0 \uad6c\uccb4\uc801\uc778 \uc218\ub97c \uc0ac\uc6a9\ud558\ub358 \uc0ac\ub78c\ub4e4\uc5d0\uac8c \uc5b4\ub835\uac8c \ubcf4\uc77c \uc218\ub3c4 \uc788\uc9c0\ub9cc, \uadf8 \uae30\ud638\uac00 \ubb34\uc5c7\uc744 \uc758\ubbf8\ud558\ub294\uc9c0\uc640 \uc0c1\uad00\uc5c6\uc774 \uc77c\uc815\ud55c \uacf5\uc2dd \ub610\ub294 \ubc29\ubc95\uc744 \ub530\ub77c \ubcc0\ud615\uc744 \ud558\uba74 \ub418\uae30 \ub54c\ubb38\uc5d0 \ub300\uc218\ud559\uc758 \ubb38\uc81c\ub294 \ucef4\ud4e8\ud130\ub3c4 \uc27d\uac8c \ud560 \uc218 \uc788\ub294 \ub2e8\uc21c\ud55c \uc791\uc5c5\ub3c4 \ub9ce\ub2e4.<\/p>\n<p>\uc2e4\uc81c\ub85c \ub300\uc218\ud559\uc5d0\uc11c \uc0ac\uc6a9\ud558\ub294 \uac00\uc7a5 \uae30\ubcf8\uc801\uc778 \uaddc\uce59(\uacf5\ub9ac)\uc740 10\uac1c\ub97c \ub118\uc9c0 \uc54a\ub294\ub2e4.<\/p>\n<p>\uc5b4\uca0b\ub4e0 \ub300\uc218\ud559\uc740 <strong>\ubaa8\ub4e0 \uc218<\/strong> \ub610\ub294 <strong>\ud2b9\uc815\ud55c \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub294 \ubaa8\ub4e0 \uc218<\/strong>\uc5d0\uc11c \uc131\ub9bd\ud558\ub294 \ub4f1\uc2dd, \ubd80\ub4f1\uc2dd \ub4f1\uc744 \ubc1d\ud78c\ub2e4.<\/p>\n<h3>\uadf8\ub798\ub514\uc5b8\ud2b8\ub97c \uc124\uba85\ud574 \ub2ec\ub77c\uace0?!!!<\/h3>\n<p>\uc11c\ub860\uc774 \uae38\uc5c8\ub2e4. <strong>\uadf8\ub798\ub514\uc5b8\ud2b8<\/strong>\ub780 \ub2e4\ubcc0\uc218 \ud568\uc218\uc758 <strong>\ubaa8\ub4e0 \uc785\ub825\uac12<\/strong>\uc5d0\uc11c <strong>\ubaa8\ub4e0 \ubc29\ud5a5<\/strong>\uc5d0 \ub300\ud55c <strong>\uc21c\uac04\ubcc0\ud654\uc728<\/strong>\uc774\ub2e4.<\/p>\n<p>\uadf8\ub798\ub514\uc5b8\ud2b8\ub97c \uacc4\uc0b0\ud558\uae30 \uc704\ud574\uc11c\ub294 \uc77c\ub2e8 \ud568\uc218\uac00 \ud544\uc694\ud558\ub2e4. <\/p>\n<p>\uc6b0\uc120 1\ucc28\uc6d0 \ud568\uc218\uc5d0 \ub300\ud55c \ubbf8\ubd84\uc744 \uc0dd\uac01\ud574\ubcf4\uc790. \uba87\uba87 \uc0ac\ub78c\ub4e4\uc740 \ubbf8\ubd84\uc744 \ub2e8\uc21c\ud788 \uae30\uc6b8\uae30\ub77c\uace0 \ub9d0\ud558\ub294\ub370, \ud568\uc218\ub97c \ubbf8\ubd84\ud55c \uacb0\uacfc\ub294 \uae30\ud558\ud559\uc801\uc778 \uae30\uc6b8\uae30\ub97c \uacc4\uc0b0\ud560 \uc218 \uc788\ub294 \ud568\uc218\uc774\ub2e4.<\/p>\n<p>\uc608\ub97c \ub4e4\uc5b4 \\(f(x)=x^2\\) \uc758 \ubbf8\ubd84 \ud568\uc218\uc778 \\(f'(x)=2x\\) \ub294 \uc810 0\uc5d0\uc11c \uae30\uc6b8\uae30\uac00 0, \uc810 1\uc5d0\uc11c\ub294 \uae30\uc6b8\uae30\uac00 \\(2\\cdot 1= 2\\) \uc784\uc744 \uc54c\ub824\uc8fc\uace0, \uc774 \ud568\uc218\ub294 \ubaa8\ub4e0 \uc810\uc5d0\uc11c\uc758 \uae30\uc6b8\uae30(\uc21c\uac04\ubcc0\ud654\uc728)\uc744 \uc54c\ub824\uc8fc\ub294 \ud568\uc218\uc774\ub2e4. (\uc5b4\ub5bb\uac8c \ubcc0\uc218\ub97c \ud65c\uc6a9\ud558\uc5ec <strong>\ubaa8\ub4e0 \uc785\ub825\uac12<\/strong>\uc5d0 \ub300\ud574 \uc21c\uac04\ubcc0\ud654\uc728\uc744 \uc54c\ub824\uc8fc\ub294\uc9c0 \uc74c\ubbf8\ud574\ubcf4\uc790.)<\/p>\n<p>\uadf8\ub798\ub514\uc5b8\ud2b8\ub294 \uc8fc\uc5b4\uc9c4 \ub2e4\ubcc0\uc218 \ud568\uc218\uc5d0 \ub300\ud574 \ubca1\ud130 \ud568\uc218\uac00 \ub41c\ub2e4. \ud2b9\uc815\ud55c \uc785\ub825\uac12\uc5d0 \ub300\ud574 \ubca1\ud130\ub97c \uc0b0\ucd9c\ud558\ubbc0\ub85c \ud655\uc2e4\ud788 \uc21c\uac04\ubcc0\ud654\uc728\uc774\ub77c\uace0 \ub9d0\ud558\uae30\uc5d4 \uc5b4\ub518\uac00 \ubd80\uc871\ud558\ub2e4.<\/p>\n<p>\uadf8\ub798\ub514\uc5b8\ud2b8\ub294 \uc815\ud655\ud55c \uc758\ubbf8\ub294 \ub2e4\uc74c\uc758 \uc2dd\uc5d0\uc11c \uc880 \ub354 \uc0b4\ud3b4\ubcfc \uc218 \uc788\ub2e4. <\/p>\n<p>\\[f(\\vec{x}+\\vec{\\epsilon}) \\approx f(\\vec{x}) + \\nabla f(\\vec{x}) \\cdot \\vec{\\epsilon}\\]<\/p>\n<p>\uc810 \\(\\vec{x}\\) \uc5d0\uc11c \ub9e4\uc6b0 \uc791\uc740 \\(\\vec{\\epsilon}\\) \uc5d0 \ub300\ud574 \uc704\uc758 \ub4f1\uc2dd\uc774 \uc131\ub9bd\ud55c\ub2e4. (\uc65c\ub0d0\ud558\uba74 \uadf8\ub798\ub514\uc5b8\ud2b8\ub97c \uc815\uc758\ud560 \ub54c \uc800\uac8c \uc131\ub9bd\ud558\ub3c4\ub85d \ud588\uae30 \ub54c\ubb38\uc774\uace0 \uc800\ub7f0 \uc2dd\uc774 \uc131\ub9bd\ud558\uc9c0 \uc54a\ub294\ub2e4\uba74 <strong>\uadf8\ub798\ub514\uc5b8\ud2b8\uac00 \uc874\uc7ac\ud558\uc9c0 \uc54a\ub294\ub2e4<\/strong>.)<\/p>\n<p>\uc800 \uc2dd\uc5d0 \ub530\ub974\uba74 \ud2b9\uc815\ud55c \ubc29\ud5a5\uc758 \uc21c\uac04\ubcc0\ud654\uc728\uc744 \uc54c\uace0 \uc2f6\ub2e4\uba74 \\(\\vec{\\epsilon}\\) \ub300\uc2e0\uc5d0 \uadf8 \ubc29\ud5a5\uc758 \uae38\uc774\uac00 1\uc778 \ubca1\ud130\ub97c \ub300\uc785\ud558\uba74 \ub41c\ub2e4. \uadf8\ub9ac\uace0 \uc5b4\ub5a4 \ubc29\ud5a5\uc5d0 \ub300\ud574\uc11c\ub3c4 \uac00\ub2a5\ud558\ub2e4.<\/p>\n<p>\uc608\ub97c \ub4e4\uc5b4\ubcf4\uc790. \\(f(x_1, x_2) = x_1^2 +x_1x_2+ x_2^2\\) \uc5d0\uc11c \\(\\nabla{f}=(2x_1+x_2, 2x_2+x_1)^\\textrm{T}\\) \uc774\uace0, \\((0,1)\\) \uc5d0\uc11c \\(\\nabla{f}(0,1)=(1,2)\\) \uc774\ub2e4. \uc774\ub54c \\((1,1)\\) \ubc29\ud5a5\uc758 \uc21c\uac04 \ubcc0\ud654\uc728\uc744 \uc54c\uace0 \uc2f6\ub2e4\uba74, \\((1,2)\\cdot (1\/\\sqrt{2},1\/\\sqrt{2})=3\/\\sqrt{2}\\) \uac00 \ub41c\ub2e4. <\/p>\n<p>\uc5b4\ub5a4 \ubc29\ud5a5\uc73c\ub85c\uc758 \uc21c\uac04\ubcc0\ud654\uc728\uc774\ub780 1\ubcc0\uc218 \ud568\uc218\ub97c \uc0dd\uac01\ud574\ubcf4\uba74 \uc26c\uc6b8 \uc218 \uc788\ub2e4. <\/p>\n<p>\\((1,1)\\) \ubc29\ud5a5\uc73c\ub85c \\((x_1, x_2)\\) \uac00 \ubcc0\ud55c\ub2e4\uba74, \\((x_1, x_2) = t(1,1) = (t,t)\\) \ub85c \uc4f8 \uc218 \uc788\ub2e4. \uc774\ub294 \\((0,0)\\) \uc744 \uc9c0\ub098\uac00\ub294 \uacbd\uc6b0\uc774\uace0, \\((0,1)\\) \uc744 \uc9c0\ub098\uac00\ub824\ud55c\ub2e4\uba74 \\((x_1, x_2) = (t,t)+(0,1)\\) \ub85c \uc4f8 \uc218 \uc788\ub2e4. \uadf8\ub54c \\(f(x_1, x_2) = x_1^2+x_1x_2+x_2^2=t^2+t\\cdot(t+1)+(t+1)^2\\) \uc774 \ub41c\ub2e4.<\/p>\n<p>\\(f(x_1,x_2)=f(t)=t^2+t(t+1)+(t+1)^2=t^2+t^2+t+t^2+2t+1=3t^2+3t+1\\) \uc774 \ub418\uace0, \uc774\ub97c \ubbf8\ubd84\ud558\uba74, \\(f'(t) = 6t+3\\) \uc774\ub2e4. \uc810 \\((0,1)\\) \uc740 \\(t=0\\) \uc77c \ub54c \uc9c0\ub098\uac04\ub2e4. \\(f'(0)=3\\) . <\/p>\n<p>\uadf8\ub7f0\ub370 \\(t\\) \uac00 \\(1\\) \ub9cc\ud07c \uc6c0\uc9c1\uc77c \ub54c \\((t,t+1)\\) \uc740 \uae38\uc774 \\(\\sqrt{2}\\) \ub9cc\ud07c \uc6c0\uc9c1\uc774\ubbc0\ub85c \uc774\ub97c \ubcf4\uc815\ud558\uba74 \\(f(t)\\) \uc758  \uc21c\uac04\ubcc0\ud654\uc728(\ub2e4\uc2dc \ub9d0\ud574 \\(f(\\vec{x})\\) \uc758 \\((1,1)\\) \ubc29\ud5a5 \uc21c\uac04\ubcc0\ud654\uc728)\uc740 \\(3\/\\sqrt{2}\\) \uac00 \ub41c\ub2e4!<\/p>\n<p><img src=\"http:\/\/141.164.34.82\/wp-content\/uploads\/2019\/10\/gradient_01.png\" alt=\"\"\/><\/p>\n<p><img src=\"http:\/\/141.164.34.82\/wp-content\/uploads\/2019\/10\/gradient_02.png\" alt=\"\"\/><\/p>\n<p><img src=\"http:\/\/141.164.34.82\/wp-content\/uploads\/2019\/10\/gradient_03.png\" alt=\"\"\/><\/p>\n<pre># cocalc.com\n# Sage Worksheet\nvar(&#39;x y z&#39;)\np1 = implicit_plot3d(x^2+x*y+y^2==z, (x,-3,3), (y,-3,3), (z,-3,3), texture=&#39;blue&#39;, mesh=True)\np2 = implicit_plot3d(x+2*(y-1)==(z-1), (x,-3,3), (y,-3,3), (z,-3,3), texture=&#39;red&#39;, mesh=True)\np3 = implicit_plot3d(x==0, (x,-3,3), (y,-3,3), (z,-3,3), alpha=0.2)\np4 = implicit_plot3d(y==1, (x,-3,3), (y,-3,3), (z,-3,3), alpha=0.2)\np1 + p2 + p3 + p4\n<\/pre>\n<p>\ub2e4\ub978 \ubc29\ud5a5\uc73c\ub85c\uc758 \uc21c\uac04\ubcc0\ud654\uc728\ub3c4 \uacc4\uc0b0\ud574\ubcf4\uc790. \uadf8\ub798\ub514\uc5b8\ud2b8\ub85c \uacc4\uc0b0\ud574\ubcf4\uace0, \uc774\ubcc0\uc218 \ud568\uc218\ub97c 1\ubcc0\uc218 \ud568\uc218\ub85c \ub9cc\ub4e4\uc5b4\uc11c\ub3c4 \uacc4\uc0b0\ud574 \ubcf4\uc790.<\/p>\n<h3>\ubaa8\ub4e0 \uac12\uc5d0\uc11c \ubaa8\ub4e0 \ubc29\ud5a5\uc758 \uc21c\uac04\ubcc0\ud654\uc728\uc744 \\(\\nabla{f}(\\vec{x})\\cdot\\vec{\\epsilon}\\) \ub85c \uad6c\ud560 \uc218 \uc788\ub2e4\uace0?<\/h3>\n<p>\uadf8\ub807\ub2e4! \\(|\\vec{\\epsilon}|=1\\) \uc774\uace0, \uadf8\ub798\ub514\uc5b8\ud2b8\uac00 \uc874\uc7ac\ud55c\ub2e4\uba74, \\(\\nabla{f}(\\vec{x})\\cdot\\vec{\\epsilon}\\) \uc740 \ubaa8\ub4e0 \uc810 \\(\\vec{x}\\) \uc5d0\uc11c \ubaa8\ub4e0 \ubc29\ud5a5 \\(\\vec{\\epsilon}\\) \uc5d0 \ub300\ud55c \uc21c\uac04\ubcc0\ud654\uc728\uc744 \ub098\ud0c0\ub0b8\ub2e4. \uc5b4\ub5bb\uac8c \uadf8\uac8c \uac00\ub2a5\ud558\ub0d0\uace0? \uadf8\ub798\ub514\uc5b8\ud2b8\uc758 \ud2b9\uc9d5\uc774\uace0 \ubcc0\uc218\uc758 \ud45c\ud604\ub825\uc774\ub2e4!<\/p>\n<p>\ub9cc\uc57d \\(|\\vec{\\epsilon}|=1\\) \uc744 \ub9cc\uc871\ud558\uc9c0 \uc54a\ub294\ub2e4\uba74 \\(\\nabla{f}(\\vec{x})\\cdot\\vec{\\epsilon}\\) \ub294 \uc785\ub825\uac12 \\(\\vec{x}\\) \uc5d0\uc11c\uc758 \uc21c\uac04\ubcc0\ud654\uc728\uc744 \uadf8\ub300\ub85c \uc720\uc9c0\ud558\uba74\uc11c \\(\\vec{\\epsilon}\\) \ub9cc\ud07c \uc785\ub825\uac12\uc744 \ubcc0\ud654\uc2dc\ud0ac \ub54c\uc758 \ubcc0\ud654<strong>\ub7c9<\/strong>\uc774\ub77c\uace0 \ub9d0\ud560 \uc218 \uc788\uaca0\ub2e4.<\/p>\n<p>\uadf8\ub9ac\uace0 \uc774\ub7f0 \ub9e5\ub77d\uc5d0\uc11c \\(f\\) \uc758 \\(\\vec{x}\\) \uc5d0\uc11c \uc21c\uac04\ubcc0\ud654\uc728\uc744 \uae30\uc900\uc73c\ub85c \uac00\uc7a5 \ube60\ub974\uac8c \\(f\\) \ub97c \ubcc0\ud654\uc2dc\ud0a4\ub294 \ubc29\ud5a5\uc740 \\(\\frac{\\nabla f(\\vec{x})}{|\\nabla f(\\vec{x})|}\\) \uc774\uace0(\ubc29\ud5a5\uc744 \ub098\ud0c0\ub0bc \ub54c\uc5d0\ub294 \ubcf4\ud1b5 \uae38\uc774 1\uc778 \ubca1\ud130\ub97c \uc0ac\uc6a9\ud55c\ub2e4), \uadf8\ub54c \uc21c\uac04 \ubcc0\ud654\uc728\uc740 \\(\\nabla f(\\vec{x}) \\cdot \\frac{\\nabla f(\\vec{x})}{|\\nabla f(\\vec{x})|}\\) \uc774 \ub41c\ub2e4. (\ub530\ub77c\uc11c \\(\\nabla f(\\vec{x}) \\cdot \\frac{\\nabla f(\\vec{x})}{|\\nabla f(\\vec{x})|}\\) \ub294 \uc785\ub825\uac12 \\(\\vec{x}\\) \uc5d0\uc11c \ud568\uc218 \\(f\\) \uc758 <strong>\ucd5c\ub300<\/strong> \uc21c\uac04\ubcc0\ud654\uc728\uc774\ub77c\uace0\ub3c4 \ud560 \uc218 \uc788\ub2e4.)<\/p>\n<p>\uc5ec\uae30\uc11c \\(\\frac{\\nabla f(\\vec{x})}{|\\nabla f(\\vec{x})|}\\) \uc740 \\(\\frac{\\vec{a}}{|\\vec{a}|}\\) \uc740 \ubca1\ud130 \\(\\vec{a}\\) \uc640 \ubc29\ud5a5\uc774 \uac19\uace0, \ud06c\uae30\ub294 1\uc778 \ubca1\ud130\uac00 \ub428\uc744 \ud65c\uc6a9\ud55c \uac83\uc774\ub2e4.<\/p>\n<h2>R\uc5d0\uc11c \uadf8\ub798\ub514\uc5b8\ud2b8 \uad6c\ud558\uae30<\/h2>\n<p>R\uc5d0\uc11c \ubbf8\ubd84 \ub610\ub294 \uadf8\ub798\ub514\uc5b8\ud2b8\ub97c \uad6c\ud558\ub294 \uae30\ubcf8\uc801\uc778 \ud568\uc218\ub294 <code>stats::D<\/code>, <code>stats::deriv<\/code>\uac00 \uc788\ub2e4.<\/p>\n<p><code>?D<\/code> \ub610\ub294 <code>?deriv<\/code>\ub97c \uccd0\ubcf4\uba74, Symbolic and Alorithmic Derivatives of Simple Expressions\ub77c\uace0 \ub098\uc628\ub2e4. \uc5ec\uae30\uc11c Simple Expressions\ub294 <code>+<\/code>, <code>-<\/code>, <code>*<\/code>, <code>\/<\/code>, <code>^<\/code>, <code>exp<\/code>, <code>log<\/code>, <code>sin<\/code>, <code>cos<\/code>, <code>tan<\/code>, <code>sinh<\/code>, <code>cosh<\/code>, <code>sqrt<\/code>, <code>pnorm<\/code>, <code>dnorm<\/code>, <code>asin<\/code>, <code>acos<\/code>, <code>atan<\/code>, <code>gamma<\/code>, <code>lgamma<\/code>, <code>digamma<\/code>, <code>trigamma<\/code>, <code>psigamma<\/code>(\uccab \ubc88\uc9f8 \uc778\uc790\uc5d0 \ub300\ud574\uc11c), <code>log1p<\/code>, <code>expm1<\/code>, <code>log2<\/code>, <code>log10<\/code>, <code>cospi<\/code>, <code>sinpi<\/code>, <code>tanpi<\/code>, <code>factorial<\/code>, <code>lfactorial<\/code>\uc744 \ud3ec\ud568\ud558\ub294 \uc218\uc2dd\uc774\ub2e4.<\/p>\n<p>\ub2e4\uc74c\uc740 <code>D<\/code> \ub610\ub294 <code>deriv<\/code>\ub97c \uc0ac\uc6a9\ud558\uc5ec \uac04\ub2e8\ud55c \ud568\uc218\uc758 \ubbf8\ubd84\uc744 \uad6c\ud558\ub294 \uc608\uc774\ub2e4.<\/p>\n<pre><code class=\"r\">expr &lt;- expression(x^2+2*x*y+y^2)\nD(expr, name=&#39;x&#39;)\n<\/code><\/pre>\n<pre>## 2 * x + 2 * y\n<\/pre>\n<pre><code class=\"r\">deriv(expr, namevec=c(&#39;x&#39;, &#39;y&#39;))\n<\/code><\/pre>\n<pre>## expression({\n##     .expr2 &lt;- 2 * x\n##     .expr8 &lt;- .expr2 + 2 * y\n##     .value &lt;- x^2 + .expr2 * y + y^2\n##     .grad &lt;- array(0, c(length(.value), 2L), list(NULL, c(&quot;x&quot;, \n##         &quot;y&quot;)))\n##     .grad[, &quot;x&quot;] &lt;- .expr8\n##     .grad[, &quot;y&quot;] &lt;- .expr8\n##     attr(.value, &quot;gradient&quot;) &lt;- .grad\n##     .value\n## })\n<\/pre>\n<h3><code>expression<\/code>, <code>quote<\/code>, \uadf8\ub9ac\uace0 <code>parse<\/code><\/h3>\n<p>R\uc5d0\uc11c expression\uc740 \uc544\uc9c1 \uacc4\uc0b0\ub418\uc9c0 \uc54a\uc740 \uc218\uc2dd\uc774\ub77c\uace0 \uc0dd\uac01\ud560 \uc218 \uc788\ub2e4. \uc608\ub97c \ub4e4\uc5b4 <code>2*x+y<\/code>\ub97c \uc785\ub825\ud558\uba74 <code>x<\/code>\uc758 \uac12\uacfc <code>y<\/code>\uc758 \uac12\uc774 \ub300\uc785\ub418\uc5b4 <code>2*x+y<\/code>\uc758 \uacb0\uacfc\uac00 \uc0b0\ucd9c\ub41c\ub2e4.<\/p>\n<pre><code class=\"r\">x=3; y=2\n2*x+y\n<\/code><\/pre>\n<pre>## [1] 8\n<\/pre>\n<p>\ub9cc\uc57d <code>x<\/code>\uc640 <code>y<\/code>\uc5d0 \uac12\uc774 \ub300\uc785\ub418\uc9c0 \uc54a\uc740 \uc218\uc2dd\uc744 \uadf8\ub300\ub85c \uc800\uc7a5\ud558\uace0 \uc2f6\ub2e4\uba74, <code>expression<\/code> \ub610\ub294 <code>quote<\/code>\ub97c \uc0ac\uc6a9\ud55c\ub2e4.<\/p>\n<pre><code class=\"r\">a &lt;- expression(2*x+y)\nprint(a)\n<\/code><\/pre>\n<pre>## expression(2 * x + y)\n<\/pre>\n<p>\uadf8\ub9ac\uace0 \uc774 \uc218\uc2dd\uc5d0 \ub530\ub77c \uc2e4\uc81c \uacc4\uc0b0\uc744 \ud558\uace0 \uc2f6\ub2e4\uba74, <code>eval<\/code> \ud568\uc218\ub97c \uc0ac\uc6a9\ud55c\ub2e4.<\/p>\n<pre><code class=\"r\">eval(a)\n<\/code><\/pre>\n<pre>## [1] 8\n<\/pre>\n<pre><code class=\"r\">x=2; y=2;\neval(a)\n<\/code><\/pre>\n<pre>## [1] 6\n<\/pre>\n<h3><code>D<\/code><\/h3>\n<p>\ud568\uc218 <code>D<\/code>\ub294 expression\uc5d0 \ub300\ud574 \ud55c \ubcc0\uc218\uc758 \ud3b8\ubbf8\ubd84\uc744 \uad6c\ud55c \uacb0\uacfc\ub97c expression\uc73c\ub85c \ubc18\ud658\ud55c\ub2e4.<\/p>\n<pre><code class=\"r\">D(expression(y*cos(x)+x*sin(y)), &#39;x&#39;)\n<\/code><\/pre>\n<pre>## sin(y) - y * sin(x)\n<\/pre>\n<p>\ub9cc\uc57d \ud2b9\uc815 \uc785\ub825\uac12\uc5d0\uc11c\uc758 \ubbf8\ubd84\uac12\uc744 \uad6c\ud558\uace0 \uc2f6\ub2e4\uba74, <code>eval(   , list(x=, y=))<\/code>\ub97c \uc0ac\uc6a9\ud560 \uc218 \uc788\ub2e4.<\/p>\n<pre><code class=\"r\">f &lt;- expression(y*cos(x)+x*sin(y))\ndfdx &lt;- D(f, &#39;x&#39;)\neval(dfdx, list(x=1, y=pi))\n<\/code><\/pre>\n<pre>## [1] -2.643559\n<\/pre>\n<p>\uc704\uc758 \\(-2.643559\\) \ub294 \\(y\\cos(x)+x\\sin(y)\\) \uc758 \\(x\\) \ud3b8\ubbf8\ubd84 \\(\\frac{\\partial f(x,y)}{\\partial x} = \\sin(y)-y\\sin(x)\\) \uc758 \\((x,y)=(1,\\pi)\\) \uc5d0\uc11c\uc758 \uac12\uc774\ub2e4.<\/p>\n<p>\\[\\frac{\\partial f(x,y)}{\\partial x}\\vert_{(x,y)=(1,\\pi)} = \\sin(\\pi)-\\pi\\sin(1) \\approx -2.643559\\]<\/p>\n<h3><code>deriv<\/code><\/h3>\n<p><code>deriv<\/code> \ud568\uc218\ub3c4 expression\uc744 \ubc1b\uc544 expression\uc744 \ubc18\ud658\ud558\ub294\ub370, \uc774 expression\uc740 <code>x<\/code>\uc640 <code>y<\/code>\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ud568\uc218\uac12\uacfc \uadf8\ub798\ub514\uc5b8\ud2b8\ub97c \ubaa8\ub450 \uad6c\ud574 \ud558\ub098\uc758 \ubcc0\uc218\ub85c \ubc18\ud658\ud55c\ub2e4.<\/p>\n<pre><code class=\"r\">f &lt;- expression(y*cos(x)+x*sin(y))\nf2 &lt;- deriv(f, c(&#39;x&#39;, &#39;y&#39;))\nf2\n<\/code><\/pre>\n<pre>## expression({\n##     .expr1 &lt;- cos(x)\n##     .expr3 &lt;- sin(y)\n##     .value &lt;- y * .expr1 + x * .expr3\n##     .grad &lt;- array(0, c(length(.value), 2L), list(NULL, c(&quot;x&quot;, \n##         &quot;y&quot;)))\n##     .grad[, &quot;x&quot;] &lt;- .expr3 - y * sin(x)\n##     .grad[, &quot;y&quot;] &lt;- .expr1 + x * cos(y)\n##     attr(.value, &quot;gradient&quot;) &lt;- .grad\n##     .value\n## })\n<\/pre>\n<p>\uc774\ub97c \ud65c\uc6a9\ud558\ub294 \ubc29\ubc95\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n<pre><code class=\"r\">eval(f2, list(x=1, y=pi))\n<\/code><\/pre>\n<pre>## [1] 1.69741\n## attr(,&quot;gradient&quot;)\n##              x          y\n## [1,] -2.643559 -0.4596977\n<\/pre>\n<p>\\(y\\cos(x)+x\\sin(y)\\) \uc758 \\((x,y)=(1,\\pi)\\) \uc5d0\uc11c\uc758 \uac12\uc740 \\(1.69741\\) \uc774\uba70, \uadf8\ub798\ub514\uc5b8\ud2b8\ub294 \\((-2.643559, -0.4596977)\\) \uc784\uc744 \uc704\uc758 \uacb0\uacfc\ub85c \uc54c \uc218 \uc788\ub2e4.<\/p>\n<p>\ud5e4\uc2dc\uc548\uae4c\uc9c0 \uad6c\ud558\uace0\uc790 \ud55c\ub2e4\uba74, <code>deriv3<\/code>\uc744 \uc0ac\uc6a9\ud55c\ub2e4. <\/p>\n<pre><code class=\"r\">f3 &lt;- deriv3(f, c(&#39;x&#39;, &#39;y&#39;))\neval(f3, list(x=1, y=pi))\n<\/code><\/pre>\n<pre>## [1] 1.69741\n## attr(,&quot;gradient&quot;)\n##              x          y\n## [1,] -2.643559 -0.4596977\n## attr(,&quot;hessian&quot;)\n## , , x\n## \n##             x         y\n## [1,] -1.69741 -1.841471\n## \n## , , y\n## \n##              x             y\n## [1,] -1.841471 -1.224606e-16\n<\/pre>\n<h3>\uadf8 \ubc16\uc5d0<\/h3>\n<p>\ub2e4\uc74c\uc5d0\uc11c \ubcf4\ub4ef\uc774 <code>expression<\/code>, <code>quote<\/code>, <code>parse<\/code>\ub294 \ubaa8\ub450 \ube44\uc2b7\ud55c \uc5ed\ud560\uc744 \ud558\uace0 \uc788\ub2e4.<\/p>\n<pre><code class=\"r\">D(expression(x^2*y), &#39;x&#39;)\nD(quote(x^2*y), &#39;x&#39;)\nD(parse(text=&quot;x^2*y&quot;), &#39;x&#39;)\n<\/code><\/pre>\n<pre>## 2 * x * y\n## 2 * x * y\n## 2 * x * y\n<\/pre>\n<p>\uc880 \ub354 <code>expression<\/code>\uacfc <code>quote<\/code>\uc740 \ub2e4\uc74c\uacfc \uac19\uc740 \ucc28\uc774\uac00 \uc788\ub2e4.<\/p>\n<pre><code class=\"r\">expression(x^2+y^2, 2*x*y)\n<\/code><\/pre>\n<pre>## expression(x^2 + y^2, 2 * x * y)\n<\/pre>\n<pre><code class=\"r\">quote(x^2+y^2, 2*x*y)\n<\/code><\/pre>\n<pre>## Error in quote(x^2 + y^2, 2 * x * y): 2 arguments passed to &#39;quote&#39; which requires 1\n<\/pre>\n<pre><code class=\"r\">quote(x^2+y^2)\n<\/code><\/pre>\n<pre>## x^2 + y^2\n<\/pre>\n<pre><code class=\"r\">a &lt;- expression(x^2+y^2, 2*x*y)\nb &lt;- quote(x^2+y^2)\nall.equal(a[[1]], b)\n<\/code><\/pre>\n<pre>## [1] TRUE\n<\/pre>\n<h2>R\uc5d0\uc11c \uc218\uce58 \ubbf8\ubd84<\/h2>\n<p>\ud568\uc218 <code>D<\/code>\uc640 \ud568\uc218 <code>deriv<\/code>\ub294 \uc55e\uc5d0\uc11c \uc5b8\uae09\ub41c \ud568\uc218\uc5d0 \ub300\ud574\uc11c\ub9cc \ubbf8\ubd84\uc774 \uac00\ub2a5\ud558\ub2e4\ub294 \ub2e8\uc810\uc774 \uc788\ub2e4. \uc218\uce58 \ubbf8\ubd84\uc744 \uc0ac\uc6a9\ud558\uba74 \uadf8\ub7f0 \uc81c\uc57d\uc740 \uc5c6\ub2e4. \ubc18\uba74 \ud55c \uc810\uc5d0 \ub300\ud574\uc11c\ub9cc \uacc4\uc0b0\uc774 \uac00\ub2a5\ud558\uba70 <code>D<\/code>\uc640 <code>deriv<\/code>\ucc98\ub7fc \ubaa8\ub4e0 \uc810\uc5d0\uc11c\uc758 \uae30\uc6b8\uae30\ub97c \uad6c\ud558\ub294 \ud568\uc218\ub97c \uad6c\ud558\uc9c0\ub294 \ubabb\ud55c\ub2e4.<\/p>\n<p>\ub2e4\uc74c\uc740 \ud568\uc218 \\(y\\cos(x)+x\\sin(y)\\) \uc758 \\((1,\\pi)\\) \uc5d0\uc11c \uadf8\ub798\ub514\uc5b8\ud2b8 \uac12\uc744 \uad6c\ud55c\ub2e4. <\/p>\n<pre><code class=\"r\">library(numDeriv)\n\nf&lt;-function(x) {x[2]*cos(x[1])+x[1]*sin(x[2])}\n\ngrad(f,c(1, pi))\n<\/code><\/pre>\n<pre>## [1] -2.6435591 -0.4596977\n<\/pre>\n<p>\ub364\uc73c\ub85c \ud5e4\uc2dc\uc548\uacfc \uc790\ucf54\ube44\uc548\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n<pre><code class=\"r\">hessian(f,c(1,pi))\n<\/code><\/pre>\n<pre>##           [,1]          [,2]\n## [1,] -1.697410 -1.841471e+00\n## [2,] -1.841471 -2.082973e-13\n<\/pre>\n<pre><code class=\"r\">g = function(x) { c(x[2]*cos(x[1])+x[1]*sin(x[2]), x[1]^2+x[2]^2)}\njacobian(g, c(1,pi))\n<\/code><\/pre>\n<pre>##           [,1]       [,2]\n## [1,] -2.643559 -0.4596977\n## [2,]  2.000000  6.2831853\n<\/pre>\n<h3><code>deriv<\/code>\uc640 <code>grad<\/code> \ube44\uad50<\/h3>\n<p>R\uc758 \ud568\uc218 <code>dgamma<\/code>\ub294 \ub2e4\uc74c\uc758 \ud568\uc218\ub97c \ub098\ud0c0\ub0b8\ub2e4. (\uc774\ub54c \\(k\\) = <code>shape<\/code>, \\(\\theta\\) = <code>scale<\/code>)<\/p>\n<p>\\[f(x; k, \\theta) = x^{k-1}\\frac{\\exp(-x\/\\theta)}{\\theta^k \\Gamma(k)}\\]<\/p>\n<pre><code class=\"r\">curve(dgamma(x, shape=2, scale=2), xlim=c(0,10))\n<\/code><\/pre>\n<p><img src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfgAAAH4CAMAAACR9g9NAAAAflBMVEUAAAAAADoAAGYAOjoAOpAAZrY6AAA6ADo6AGY6OmY6OpA6ZrY6kNtmAABmADpmAGZmOgBmOpBmZmZmZrZmtv+QOgCQOjqQOmaQZgCQtpCQ29uQ2\/+2ZgC2Zma2\/7a2\/\/\/bkDrb25Db\/7bb\/9vb\/\/\/\/tmb\/25D\/\/7b\/\/9v\/\/\/\/UrAd4AAAACXBIWXMAAAsSAAALEgHS3X78AAAPH0lEQVR4nO2dC3fbuBGF5a3tpt44aVor2669G7W1Xv\/\/D1aUH7EtkhoQA+AO7\/1OzvrssQjNzGcQAJ+LvaBk0ToA0QaJJ0XiSZF4UiSeFIknReJJkXhSJJ4UiSdF4kmReFIknhSJJ0XiSZF4UiSeFIknReJJkXhSJJ4UiSdF4kmReFIknhSJJ0XiSZF4UiSeFIknReJJkXhSJJ4UiSdF4kmReFIknhSJJ0XiSZF4UiSeFIknReJJkXhSJJ4UiSdF4kmReFIknhSJJ0XiSZF4UiSeFIknReJJkXhSJJ4UiSclR\/xCIFNQfMa2ojQST4rEkyLxpEg8KRJPisSTIvGkSDwpEk+KxJMi8aSEFH\/+HIM4RzjxL9IlP49g4t\/LlvrphBJ\/KlrqpxJJfG+DUj+NQOKH2pP6KYQRP6ZX6tOJIr5gnJwEEX+2LXX6RGKItzQl80mEEG9rSeZTmJF4mU8hgnhzQzJvJ4D4hHZk3gy++KRmZN7KzMTLvBV48amtyLyN2YmXeRvo4ic0IvMWJJ4UcPGT2pB5A3MUL\/MGsMVPbULmzzJP8TJ\/Fmjx01uQ+HPMVLzMnwNZfFYDMj\/ObMXL\/DjzFS\/zowCLb739vJmxeJkfA1d8y8MABMxavMwPAyu+1bk9FuYtXuYHQRXf4BJdLiSelLmLl\/kBQMU76pL5XuYvXuZ7kXhSMMX7upL5HhjEy3wPFOJl\/hRI8e6eJP4EDvEyfwKJeJn\/CKL4EpIk\/gMs4mX+AxJPCqD4Qopk\/h0STwqPeJl\/R6747dcf++3tYnH5mL7txK+cisS\/xUF8536\/+TV924lfORmZf4OD+M3N41PPT9124ldOR+Z\/ki3+9uL337oef3Oyr5d4ZPInd7vl4mq\/\/uWkw08sc1E5Mv8K3Ky+rBuZf0HiSUETX9qMzD\/DJl7mn8mf1S+eOJ3dSTwy2T1+t\/w8eVufbfC+IgL5u\/rtl\/sP27zgH44LMt8BNsZLfC0Ixct8h5d4n2P1lZTIPFqPl\/hqUIqXeQfxm+uBZTyyeJnPFr9b3h1\/rk8vwUkvbj0dEu9x6dXbnynbpn+bH\/TmSXu8zGeP8c8H613GeImvB9Ksvq4LcvMSTwqveHLzEk8KkPjqIqjNM4unNi\/xpFCLZzbPLZ7YvMSTYhO\/Ph6WvXNtOvPjTtCat4hfL666H7tlmnqJR8Ygfvvt9cTbH6enYiY3nflxL1jN44zxEl8Vi\/jN9eLivvdai5ymMz\/uBql5g\/juWovuRimJnxOWMf4o\/OGqrPh29ec0b+zxB1Z\/+TRP8ZzmLWP89vZ4Q+yq5\/KqjKazPu2KxCf\/2nHbltVnNC\/xjb+7FRLf\/MvbgCK+beklPvHXfts2Lj2feZv4zacfq6FH3UxtOuPDBWj9\/dWReIzvr47EowRQGRDxAGUHCKEmEg8UQk0k\/hWEGOoBspyDKDpEELWQ+J9ABFELDPEgJQcJowoS\/xaUOCpgE79bLi7\/+\/FhxZlNT\/xoUVDiqIBJ\/G75eXPz2PN8o5ymJ360LDCBFMck\/unlcgWvucOpN04khUno8atiPR6o2kChlMU8xve+Pjan6UmfLA9SLCWBmNVDFRsqmHJI\/EeggimH5YaK4RdN5TQ96ZM1wIqmFAg9Hq3SaPEUQeJPQYunCDbxq6K7erhCwwVUANsBnC\/366v96sq16QkfrAVcQAWwHrl7+ufZ9IQPVgMvIndsR+6+3x\/+bUrdLYtXZryI3DFferVeLBIvvrJWD7HKiDH5AjCrhywyZFCeSHw\/kEF5YhO\/XtztVxeFLsTArDFmVH5Yl3P740Dv2XTy5yoDGpYXxvPx3VNwCl2Bg1pg1LicsO3qj+dpEg\/cRRePG5gL7Sd3sPWFDcwFiR8GNzIHjCdpLh9XpR5bjlte3MgcsM7qD\/8KzeqBywscWjbWkzSHPl9GPHJxkWPLxXo+\/uJ+XWZXD11c6ODyaD65w64tdnQ5SPwo2NHlIPHjgIc3HYk\/A3p8U2ktHr6u8AFOJEH89naRdLnlPMQHiHAS6vFnCRDiBCT+LAFCnIBFfMnXj0WoaoQYkzGIL\/r6sRBFDRFkIgbx468fO+wOBm6vspQrRkljRJmGscfvh14\/9vzLvuuy5iM+SpgpWMb4sdePvewGenYHMxIfJk47ubN6jh4fKFAr2cu55+dlzHqM3wcK1ErjdXycesaJ1IbEWwkUqoW24kMVM1SwZ7GJL\/WGilC1DBXsWXLFjzwLbW7ig0V7huwe3x3MndS08SNIBAt3lPxd\/fbjc+wXL2R\/OxrBwh1FY3wK0eIdoan4eHWMF\/EQXsu5Scfq45UxXsRDNF3HByxjwJD7kfhEIsbcR7b4nAsxIhYxYsx92MQPv34s67RsyCKGDPoUk\/iR149lXYgRs4Yxo\/6ISfzI68dyenzQCgYN+wMJPb7\/9WMZF2JErWDUuN9hHuMLvH4sagGjxv2Olsu5sAUMG\/gbJH4KcSN\/JWFXn\/hmEomHxjq5O\/zX\/Z00gcsXOPRnrMu5vf9Nk6GLFzr4Dtuu\/tjZvXt86NqFDr7D1uMnvWR01uKDR990Vh+8dPMOX+KHiR2\/cYwv8YrR2IWLHr9tjC\/yitHYhdsHT8C6nCvwitHQdTsSOQPbAZwSrxiNXLUXAudgvrza\/RWjgYv2k7hJtJvVx63ZG+ImIfF5hM3CZmddYDkXtmTviZqGdTlXqun4BM0j4exckaZnQMxEjEfuku+YPNt0zHL1ETMTg\/hp5+Z4xMdMpdmsPmS1BoiYi8R7EDAZ4xjv\/27ZgLUaIV421uWc+7tl45VqjHjZWJdz7u+WjVeqUcKlY70Qw\/3dsuEqdYZo+bSa3EWr03mCZSTxXgTLSOLdiJWSxLsRKyWJ9yNUTgniXd8tG6pIViIlpR7vSaCsJN6TQFnZjtx96x5\/s\/vN78hdoAolEScv4+XV11f7h4vE668YxcdJzLqrTz5gSyo+TGbq8d4ESU1jvDsxcrNcc\/fP1\/\/9w+uJGDGKM5EQyVl6\/PrpwM1umTbO04oPkZ1tjH+6k8bxfHyE0mQQIL02B3ACFCaLAPlJfBHwE7ReeuV7QwV+XXKBz9B6la3vM3Dgy5IPeorWq2x9n4GDXhUPwHM0iXd\/Bg54UXzATtJ4yNb5GTjYNfECOkvN6guCnGbKARy3WT1yQVwBTtQ6q3dtGrgezuBmap3VuzaNWw53YFM1HsDxfRQKbDUKgJprkyN3qMUoAWquGuNLA5qsxvjiYGarMb48kOnaevzgi4OnNQ1ZiYIg5tvkyB1iIYoCmHCLI3eAZSgNXsotZvV4VSgPXM4tZvVwRagBWtItZvVoNagDWNYtjtyBlaAWWGlrjK8HVN4a4yuClLjG+JoAZd7iyB1Q+rXBSb3FkTuc7OsDk3uu+G7473YIl4\/2bWGSbwFK8rnLuZcbLTa\/2ptGyb0NINlbl3NDt1AdrG9uHnsn\/kNNg2TeDIz8rcu5oVuotrcXv3ePSDnatzWNkXhDIApgEj96C9Vuubjar3uGAYkfYgFQAtsY73oLFUDWzWlfgwbLufZJA9C8CNniN9dDM36JH6N1FVKO3PXZ3S2fHom0Pl3IS\/wojctg6\/EP3fC+uuqx+zLV13IumbZ1SDg7t\/3656ld9fjpNC2EbTm3PPb4y\/+cLtZ7TuAsXpj2lUS0rIRxcvdw8Hi1vXV5sqXEv9KwFFrONaVdLbzE2yd38v6WZtUwiH9ZzDldiCHx72hVjqTlnEvTEv+eRvVIWs719fjkI3cS\/4E2BUlazp0u5ias4yX+I01O1tl29btlt5zr+0D6kTuJP6VBTXJn9erxLtQvSvZybvjSa4lPoPruvv4BHInvp3JdJB6GuoWReByq7u6ri5f3ESoWR+KhqFcdicei2u5e4tGoVCCJh6NOp5d4QGrUSOIRqVAkiYek\/O5e4kEpXSeJR6VwoWqLl3czZXf3Eg9MyWJJPDIFO73EY1NMvcSjU6hiEg9PmU4v8QEoUTSJj0CBTi\/xMXBXL\/FRcFZfWby8Z+BaPIkPhGf1JD4Sjrt7iY+FWwElPhhenV7iw+GjXuID4qFe4kOSr17ig5KrXuLDkqe+rnh5dyVHvcSHZrp6iQ\/OVPUSH55p6iV+Bgy\/G2Bkm6xfp24r8aVIVi\/xcyFRvcTPhyT1Ej8nEgZ7iZ8ZVvcSPz9M6quKl\/dKGLq9xM+Uc+4lfr6Mqpf4OTOiXuLnzeAeX+JnT796iSegr9tLPAcn7iWeFIknReJJqSle3oGQeFIknhSJJ0XiSZF4UiSeFIknReJJkXhSJJ6UiuLlHQmJJ0XiSZF4UiSelGzxm+tFxy8\/zm4r8Ujkit8t744\/15eP57aVeCRyxW+\/\/nj3c2RbiUdCPZ6U7DF+e6sxPiKa1ZNST7y8Q1FvOSfxUNSb3Ek8FPWWcxIPhXo8KQWWc4sXUpsSFal606TAQeJJ8RJvOFYvkFCPJ0XiSal4IYZAouJpWYFExQsxBBLq8aRUvBBDIKFZPSkST4rEk1JSvECmnPhyTfk2BhtYy8YknrQxiSdtTOJJG5N40sYknrQxiSdtTAdhSJF4UiSeFIknReJJkXhSJJ4UiSdF4kmReFK8xG9vF6fXX0+lu3nnzqux1wvEXZpaXNx7NXbIsufS5YltffqR6MBJfFfc1ZVPW\/vtl\/v95q9uBV75\/RE93PXdXzCNLsuVU2Pr7k8ozYGT+O4+m+NfnQfrLvoHL1ubv\/3dq6meu4mms7l59Grw4eLfh9qnOXASf8zii1sn3fs1tvv+u9uufnPzL79dvWePPwpPc+AkvtsBeorfLT87tbT67DfGb67vjuX1wXNa1IlPc4DZ47e3Xt4PgTmK98yym8WsvWZ3zXq86xh\/7FlOrI6XmDv9GW2\/OYp33UluWo3x3a7ZbVbv6L3DcTn34Lird+\/xaQ4Q1\/FPvdRx8e3W1CFLt6X3YQ3mN1Nsto4X0ZB4UiSeFIknReJJkXhSJJ4UiSdF4kmReFIknhSJJ0XiSZF4UiSeFIknReJJkXhSJJ4UiSdF4kmReFIk\/okHx\/sCQiDxT2y\/\/ul5Kyw+Ev\/Myus+qyBI\/DOOT2IIgcQ\/8\/APqiFe4p\/Z3PzvO1WXl\/gj3Y2Vbk+3CYHEkyLxpEg8KRJPisSTIvGkSDwpEk+KxJMi8aRIPCkST4rEkyLxpEg8KRJPisSTIvGk\/B9jEv6JGc7QjwAAAABJRU5ErkJggg==\" alt=\"plot of chunk unnamed-chunk-16\"\/><\/p>\n<p>\\((x,k,\\theta) = (2, 2, 2)\\) \uc5d0\uc11c \uadf8\ub798\ub514\uc5b8\ud2b8\ub97c \uad6c\ud558\uace0\uc790 \ud55c\ub2e4.<\/p>\n<pre><code class=\"r\">deriv(expression(dgamma(x,k,th)), c(&#39;x&#39;, &#39;k&#39;, &#39;th&#39;))\n<\/code><\/pre>\n<pre>## Error in deriv.default(expression(dgamma(x, k, th)), c(&quot;x&quot;, &quot;k&quot;, &quot;th&quot;)): Function &#39;dgamma&#39; is not in the derivatives table\n<\/pre>\n<p><code>deriv<\/code>\ub85c\ub294 <code>dgamma<\/code>\uc758 \ubbf8\ubd84\uc774 \ubd88\uac00\ub2a5\ud558\uc9c0\ub9cc <code>grad<\/code>\ub97c \ud1b5\ud55c \uc218\uce58\ubbf8\ubd84\uc740 \uac00\ub2a5\ud558\ub2e4.<\/p>\n<pre><code class=\"r\">f &lt;- function(x) {\n  dgamma(x[1], x[2], x[3])\n}\ngrad(f, c(2,2,2))\n<\/code><\/pre>\n<pre>## [1] -0.2197877  0.1411784 -0.1465251\n<\/pre>\n<h2>\ud55c \uc904 \uc815\ub9ac<\/h2>\n<p><strong>\uadf8\ub798\ub514\uc5b8\ud2b8<\/strong>\ub780 \ub2e4\ubcc0\uc218 \ud568\uc218\uc758 <strong>\ubaa8\ub4e0 \uc785\ub825\uac12<\/strong>\uc5d0\uc11c <strong>\ubaa8\ub4e0 \ubc29\ud5a5<\/strong>\uc73c\ub85c\uc758  <strong>\uc21c\uac04\ubcc0\ud654\uc728<\/strong>\uc774\ub2e4. \ubaa8\ub4e0 \ubc29\ud5a5\uc758 \uc21c\uac04\ubcc0\ud654\uc728\uc740 \ud568\uc218 \\(f(\\vec{x})\\) \uc758 \uc5b4\ub5a4 \ud55c \uc810(\ud639\uc740 \ubaa8\ub4e0 \uc810)\uc5d0\uc11c \uc811\ud558\ub294 <strong>\uc811\ud3c9\uba74\uc758 \uae30\uc6b8\uae30<\/strong>\uc774\ub2e4. (\uc811\ud3c9\uba74\uc758 \uae30\uc6b8\uae30\ub294 \ubcc0\uc218 \uac2f\uc218\ub9cc\ud07c\uc758 \uc22b\uc790\uac00 \ud544\uc694\ud558\ub2e4.)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\uc9c8\ubb38: \uadf8\ub798\ub514\uc5b8\ud2b8\ub780 \ubb34\uc5c7\uc778\uac00?[1] [1]: \uc774 \uae00\uc758 \uc77c\ubd80\ub294 \ucd9c\uac04 \uc608\uc815\uc778 &lt;\uc218\ud559\uc758 \uc228\uc740 \uc6d0\ub9ac 2&gt;\uc758 \uc6d0\uace0 \uc77c\ubd80\ub97c \ubc1c\ucdcc\ud55c \uac83\uc785\ub2c8\ub2e4. \uc77c\uc804\uc5d0 facebook\uc5d0\uc11c \uadf8\ub798\ub514\uc5b8\ud2b8\uac00 \ubb34\uc5c7\uc778\uc9c0\uc5d0 \ub300\ud574 \ud55c\ucc3d \ub17c\ub780\uc774 \uc788\uc5c8\ub2e4. \uc5b4\ub5a4 \uc0ac\ub78c\ub4e4\uc740 \uadf8\ub798\ub514\uc5b8\ud2b8\uac00 \uae30\uc6b8\uae30\ub77c\uace0 \ud558\uace0, \uc5b4\ub5a4 \uc0ac\ub78c\uc740 \ub2e8\uc21c\ud788 \ubc29\ud5a5\uc774\ub77c\uace0 \ud588\ub2e4. \uadf8\ub9ac\uace4 \ub2e4\ub978 \uc0ac\ub78c\uc774 \uacf5\uc2dd \ud558\ub098\ub97c \ubcf4\uc5ec\uc8fc\ub294 \uac83\uc73c\ub85c \ud6c8\ud6c8\ud788(?) \ub9c8\ubb34\ub9ac\uac00 \ub418\uc5c8\ub2e4. (\uadf8\ub807\uc9c0! \uc218\ud559\uc774\ub780 \ubaa8\ub984\uc9c0\uae30 \uacf5\uc2dd\uc73c\ub85c \ub9d0\ud558\ub294 \uac83\uc774\ub2e4!?) \uadf8\ub7f0\ub370 \uc815\ub9d0\ub85c, \uadf8\ub798\ub514\uc5b8\ud2b8\uac00 \ubb34\uc5c7\uc778\uac00? [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2009,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[319],"tags":[398,309,399,19,400],"jetpack_featured_media_url":"http:\/\/ds.sumeun.org\/wp-content\/uploads\/2019\/10\/gradient_01.png","_links":{"self":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts\/2012"}],"collection":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2012"}],"version-history":[{"count":3,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts\/2012\/revisions"}],"predecessor-version":[{"id":2015,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/posts\/2012\/revisions\/2015"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=\/wp\/v2\/media\/2009"}],"wp:attachment":[{"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2012"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2012"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/ds.sumeun.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2012"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}