{"id":677,"date":"2024-04-20T07:55:15","date_gmt":"2024-04-20T07:55:15","guid":{"rendered":"https:\/\/gbelentzas.sites.sch.gr\/?p=677"},"modified":"2024-05-02T09:06:01","modified_gmt":"2024-05-02T09:06:01","slug":"%cf%80%ce%b1%cf%81%ce%ac%ce%b3%cf%89%ce%b3%ce%bf%cf%82-%cf%84%ce%b7%cf%82-x-%ce%bd-%ce%b1%cf%80%cf%8c%ce%b4%ce%b5%ce%b9%ce%be%ce%b7","status":"publish","type":"post","link":"https:\/\/gbelentzas.sites.sch.gr\/?p=677","title":{"rendered":"\u03a0\u03b1\u03c1\u03ac\u03b3\u03c9\u03b3\u03bf\u03c2 \u03c4\u03b7\u03c2 x^(-\u03bd), \u03cc\u03c0\u03bf\u03c5 \u03bd \u03c6\u03c5\u03c3\u03b9\u03ba\u03cc\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 (\u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7)"},"content":{"rendered":"

\u0398\u03b5\u03ce\u03c1\u03b7\u03bc\u03b1 11. <\/strong>\u0388\u03c3\u03c4\u03c9 \u03b7 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 <\/span>\"\textcolor{blue}{f(x)=x^{-\grn}, \grn \in \mathbf{N}^*.}\" \u039d\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03b7 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 f \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03af\u03c3\u03b9\u03bc\u03b7 \u03c3\u03c4\u03bf\u00a0<\/span>\"\textcolor{blue}{\mathbf{R}^*}\" \u03ba\u03b1\u03b9 \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9\u00a0<\/span>\"\textcolor{blue}{ f^{\prime}(\mathbf{x})=-\grn \mathbf{x}^{-\grn-1}}\" \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae<\/span><\/p>\n

\n
\n

  <\/span>   <\/span>\"\[\textcolor{blue}{\left(x^{-\grn}\right)^{\prime}=-\grn x^{-\grn-1} }\]\"<\/p>\n<\/div>\n<\/div>\n

\n

\u0388\u03c3\u03c4\u03c9 \u03b7 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 \"f(x)=x^{-\grn}, \grn \in \mathbf{N}^*.\"<\/p>\n

\u03a0\u03c1\u03ac\u03b3\u03bc\u03b1\u03c4\u03b9, \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 \"x\in \mathbf{R}^*\" \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 :<\/p>\n

  <\/span>   <\/span>\"\[\left(x^{-\grn}\right)^{\prime}=\left(\frac{1}{x^\grn}\right)^{\prime}=\frac{(1)^{\prime} x^\grn-1\left(x^\grn\right)^{\prime}}{\left(x^\grn\right)^2}=\frac{-\grn x^{\grn-1}}{x^{2 \grn}}=-\grn x^{-\grn-1} .\]\"<\/p>\n

\u0395\u03af\u03b4\u03b1\u03bc\u03b5, \u03cc\u03bc\u03c9\u03c2, \u03c3\u03b5 \u03c0\u03c1\u03bf\u03b7\u03b3\u03bf\u03cd\u03bc\u03b5\u03bd\u03b7 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 \u03cc\u03c4\u03b9 \"\left(x^v\right)^{\prime}=\grn x^{\grn-1}\" \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 \u03c6\u03c5\u03c3\u03b9\u03ba\u03cc \"\grn> 1.\"<\/p>\n

\u0393\u03b5\u03bd\u03b9\u03ba\u03cc\u03c4\u03b5\u03c1\u03b1, \u03b1\u03bd \"\kappa\in\mathbf{Z}-\{0,1\}\" \u03c4\u03cc\u03c4\u03b5<\/p>\n

  <\/span>   <\/span>\"\[\left(x^\kappa\right)^{\prime}=\kappa x^{\kappa-1}\]\"<\/p>\n","protected":false},"excerpt":{"rendered":"

\u0398\u03b5\u03ce\u03c1\u03b7\u03bc\u03b1 11. \u0388\u03c3\u03c4\u03c9 \u03b7 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 \u039d\u03b1 \u03b1\u03c0\u03bf\u03b4\u03b5\u03af\u03be\u03b5\u03c4\u03b5 \u03cc\u03c4\u03b9 \u03b7 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 f \u03b5\u03af\u03bd\u03b1\u03b9 \u03c0\u03b1\u03c1\u03b1\u03b3\u03c9\u03b3\u03af\u03c3\u03b9\u03bc\u03b7 \u03c3\u03c4\u03bf\u00a0 \u03ba\u03b1\u03b9 \u03b9\u03c3\u03c7\u03cd\u03b5\u03b9\u00a0 \u03b4\u03b7\u03bb\u03b1\u03b4\u03ae     \u0388\u03c3\u03c4\u03c9 \u03b7 \u03c3\u03c5\u03bd\u03ac\u03c1\u03c4\u03b7\u03c3\u03b7 \u03a0\u03c1\u03ac\u03b3\u03bc\u03b1\u03c4\u03b9, \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 \u03ad\u03c7\u03bf\u03c5\u03bc\u03b5 :     \u0395\u03af\u03b4\u03b1\u03bc\u03b5, \u03cc\u03bc\u03c9\u03c2, \u03c3\u03b5 \u03c0\u03c1\u03bf\u03b7\u03b3\u03bf\u03cd\u03bc\u03b5\u03bd\u03b7 \u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7 \u03cc\u03c4\u03b9 \u03b3\u03b9\u03b1 \u03ba\u03ac\u03b8\u03b5 \u03c6\u03c5\u03c3\u03b9\u03ba\u03cc \u0393\u03b5\u03bd\u03b9\u03ba\u03cc\u03c4\u03b5\u03c1\u03b1, \u03b1\u03bd \u03c4\u03cc\u03c4\u03b5    <\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":["post-677","post","type-post","status-publish","format-standard","hentry","category-13"],"featured_image_src":null,"author_info":{"display_name":"admin","author_link":"https:\/\/gbelentzas.sites.sch.gr\/?author=1"},"yoast_head":"\n\u03a0\u03b1\u03c1\u03ac\u03b3\u03c9\u03b3\u03bf\u03c2 \u03c4\u03b7\u03c2 x^(-\u03bd), \u03cc\u03c0\u03bf\u03c5 \u03bd \u03c6\u03c5\u03c3\u03b9\u03ba\u03cc\u03c2 \u03b1\u03c1\u03b9\u03b8\u03bc\u03cc\u03c2 (\u03b1\u03c0\u03cc\u03b4\u03b5\u03b9\u03be\u03b7) - 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