{"id":26583,"date":"2023-08-01T14:30:24","date_gmt":"2023-08-01T14:30:24","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=26583"},"modified":"2023-08-30T13:44:56","modified_gmt":"2023-08-30T13:44:56","slug":"clase-digital-8-diferencial","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-8-diferencial\/","title":{"rendered":"Clase digital 8. Diferencial"},"content":{"rendered":"\n\n\n<div class=\"wp-block-cover is-light\" style=\"min-height:284px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"wp-block-cover__background has-background-dim-40 has-background-dim\"><\/span><img decoding=\"async\" class=\"wp-block-cover__image-background wp-image-26638\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Diferencial.png\" style=\"object-position:38% 97%\" data-object-fit=\"cover\" data-object-position=\"38% 97%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1500\" height=\"700\" class=\"wp-block-cover__image-background wp-image-26638\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Diferencial.png\" style=\"object-position:38% 97%\" data-object-fit=\"cover\" data-object-position=\"38% 97%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Diferencial.png 1500w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Diferencial-300x140.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Diferencial-1024x478.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Diferencial-768x358.png 768w\" sizes=\"auto, (max-width: 1500px) 100vw, 1500px\" \/><\/noscript><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-base-3-color has-text-color has-large-font-size wp-block-paragraph\">Diferencial<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"introduccion\">Introducci\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">En esta secci\u00f3n veremos algo llamado diferencial, que aunque se parece a la derivada no es exactamente lo mismo, ser\u00e1 \u00fatil para realizar la operaci\u00f3n inversa a la derivada, simplemente es f\u00e1cil.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"desarrollo-del-tema\">Desarrollo del tema <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Diferencial<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00bfRecuerdas cuando hablamos que la derivada iba a representar la pendiente de una recta tangente en un punto de una funci\u00f3n?<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.38.15.png\" alt=\"\" class=\"wp-image-28283\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"419\" height=\"412\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.38.15.png\" alt=\"\" class=\"wp-image-28283\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.38.15.png 419w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.38.15-300x295.png 300w\" sizes=\"auto, (max-width: 419px) 100vw, 419px\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">Pues bien regresemos a ese momento, vamos a considerar la funci\u00f3n:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.39.01.png\" alt=\"\" class=\"wp-image-28285\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"933\" height=\"344\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.39.01.png\" alt=\"\" class=\"wp-image-28285\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.39.01.png 933w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.39.01-300x111.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.39.01-768x283.png 768w\" sizes=\"auto, (max-width: 933px) 100vw, 933px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>Definici\u00f3n de dy<\/em><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Si la funci\u00f3n f est\u00e1 definida por la ecuaci\u00f3n\u00a0<em>y = f(x<\/em>) entonces la diferencial de <strong>y<\/strong> denotada por <strong>dy<\/strong> est\u00e1 dada por:<\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>\u2146y = f'(x)\u0394x<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Donde x est\u00e1 en el dominio de <strong>f \u00b4<\/strong> y \u0394x , un incremento de <strong>x<\/strong>. Esto nos sirve para conocer cu\u00e1nto cambia la funci\u00f3n cuando cambia alguna de las variables.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por ejemplo:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.40.58.png\" alt=\"\" class=\"wp-image-28286\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"927\" height=\"254\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.40.58.png\" alt=\"\" class=\"wp-image-28286\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.40.58.png 927w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.40.58-300x82.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.40.58-768x210.png 768w\" sizes=\"auto, (max-width: 927px) 100vw, 927px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Dy<\/strong> es una diferencial de la variable dependiente, pero para saber la diferencial de una variable independiente, podemos recurrir a la funci\u00f3n&nbsp;<\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>y = x, donde dy = \u0394x.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><em>Definici\u00f3n de dx<\/em><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Si la funci\u00f3n <strong><em>f<\/em> <\/strong>est\u00e1 definida por la ecuaci\u00f3n<em> y = f(x)<\/em> entonces la <strong>diferencial de <em>x<\/em><\/strong><em> <\/em>denotada por <strong><em>dx<\/em><\/strong> est\u00e1 dada por:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.42.10.png\" alt=\"\" class=\"wp-image-28287\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"935\" height=\"290\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.42.10.png\" alt=\"\" class=\"wp-image-28287\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.42.10.png 935w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.42.10-300x93.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.42.10-768x238.png 768w\" sizes=\"auto, (max-width: 935px) 100vw, 935px\" \/><\/noscript><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Aplicaci\u00f3n de diferenciales<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Utilice diferenciales para aproximar el volumen de un cascar\u00f3n esf\u00e9rico cuyo radio interno mide 4 m y cuyo espesor es de 1\/16 metros.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.42.53.png\" alt=\"\" class=\"wp-image-28288\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"559\" height=\"412\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.42.53.png\" alt=\"\" class=\"wp-image-28288\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.42.53.png 559w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.42.53-300x221.png 300w\" sizes=\"auto, (max-width: 559px) 100vw, 559px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Por lo que un peque\u00f1o incremento en el radio har\u00e1 que aumente el volumen de la esfera, ese peque\u00f1o incremento del radio, formar\u00e1 el cascar\u00f3n. Para saber cu\u00e1nto cambia el volumen cuando cambia el radio, sacamos el diferencial de <strong><em>dV<\/em><\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.43.27.png\" alt=\"\" class=\"wp-image-28289\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"924\" height=\"242\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.43.27.png\" alt=\"\" class=\"wp-image-28289\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.43.27.png 924w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.43.27-300x79.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-30-a-las-7.43.27-768x201.png 768w\" sizes=\"auto, (max-width: 924px) 100vw, 924px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Te recomiendo que leas los siguientes textos, en donde se ahonda m\u00e1s en el tema y hay m\u00e1s ejemplos:<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/calculo-louis-leithold.pdf\" type=\"application\/pdf\" style=\"width:100%;height:600px\" aria-label=\"Incrustado de calculo-louis-leithold.\"><\/object><a id=\"wp-block-file--media-b40b86d6-f980-41cd-ac67-47a02098b057\" href=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/calculo-louis-leithold.pdf\">calculo-louis-leithold<\/a><a href=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/calculo-louis-leithold.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-b40b86d6-f980-41cd-ac67-47a02098b057\">Descarga<\/a><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Una vez que ha concluido con el estudio de material escrito y video, realiza la consigna.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"conclusion\">Conclusi\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">El diferencial es entonces un peque\u00f1o pero muy peque\u00f1o incremento en una funci\u00f3n. Ahora s\u00ed, pasemos a la antiderivada, ya estamos listos para integrar.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"fuentes-de-informacion\">Fuentes de informaci\u00f3n<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/luiscastellanos.files.wordpress.com\/2007\/02\/calculo-louis-leithold.pdf\">https:\/\/luiscastellanos.files.wordpress.com\/2007\/02\/calculo-louis-leithold.pdf<\/a>, p\u00e1ginas 281-287 numeraci\u00f3n del libro.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Introducci\u00f3n En esta secci\u00f3n veremos algo llamado diferencial, que aunque se parece a la derivada no es exactamente lo mismo, ser\u00e1 \u00fatil para realizar la operaci\u00f3n inversa a la derivada, simplemente es f\u00e1cil. Desarrollo del tema Diferencial \u00bfRecuerdas cuando hablamos que la derivada iba a representar la pendiente de una recta tangente en un punto &#8230; <a title=\"Clase digital 8. Diferencial\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-8-diferencial\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 8. Diferencial\">Leer m\u00e1s<\/a><\/p>\n","protected":false},"author":142,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","episode_type":"","audio_file":"","podmotor_file_id":"","podmotor_episode_id":"","cover_image":"","cover_image_id":"","duration":"","filesize":"","filesize_raw":"","date_recorded":"","explicit":"","block":"","itunes_episode_number":"","itunes_title":"","itunes_season_number":"","itunes_episode_type":"","footnotes":""},"categories":[19,685],"tags":[41,176,64],"class_list":["post-26583","post","type-post","status-publish","format-standard","hentry","category-ingenieria-en-sistemas-computacionales","category-uda-calculo-diferencial-ingenieria-en-sistemas-computacionales","tag-clase-digital","tag-monica-trejo-duran","tag-neli06002"],"acf":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/26583","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/users\/142"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/comments?post=26583"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/26583\/revisions"}],"predecessor-version":[{"id":28290,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/26583\/revisions\/28290"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=26583"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=26583"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=26583"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}