{"id":26577,"date":"2023-08-01T14:20:43","date_gmt":"2023-08-01T14:20:43","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=26577"},"modified":"2023-08-04T15:58:52","modified_gmt":"2023-08-04T15:58:52","slug":"clase-digital-5-derivadas","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-5-derivadas\/","title":{"rendered":"Clase digital 5. Derivadas"},"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-26632\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Derivadas.png\" style=\"object-position:47% 95%\" data-object-fit=\"cover\" data-object-position=\"47% 95%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1500\" height=\"700\" class=\"wp-block-cover__image-background wp-image-26632\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Derivadas.png\" style=\"object-position:47% 95%\" data-object-fit=\"cover\" data-object-position=\"47% 95%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Derivadas.png 1500w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Derivadas-300x140.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Derivadas-1024x478.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Derivadas-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\">Derivadas<\/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\">Hemos llegado al tema m\u00e1s \u00fatil en el \u00e1rea de ingenier\u00eda, f\u00edsica, qu\u00edmica y dem\u00e1s ciencias exactas, <strong>las derivadas<\/strong>. No se trata de un proceso complicado, solo te pido que memorices las f\u00f3rmulas y que hagas muchas derivadas y ver\u00e1s,que despu\u00e9s de un rato se vuelven m\u00e1s f\u00e1ciles.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La derivada se define a partir de los l\u00edmites&nbsp; y es posible realizarla en funciones continuas, por ello es que esos temas fueron revisados antes, as\u00ed que estamos listos, \u00a1adelante!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"desarrollo-del-tema\">Desarrollo del tema <\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Derivadas<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">El concepto de derivada es muy \u00fatil en diversas \u00e1reas tanto de ingenier\u00eda como en la administraci\u00f3n. La derivada tiene interpretaci\u00f3n como raz\u00f3n de cambio o tasa de cambio, pendiente de la l\u00ednea tangente a la curva en un punto. Ejemplo de ello es la velocidad, recordemos que se calcula como , o (Vf-Vo)\/intervalo de tiempo.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La forma en que se expresa una derivada puede ser de cualquiera de estas formas<\/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-2023-08-04-a-las-9.43.09.png\" alt=\"\" class=\"wp-image-26943\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"636\" height=\"256\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.43.09.png\" alt=\"\" class=\"wp-image-26943\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.43.09.png 636w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.43.09-300x121.png 300w\" sizes=\"auto, (max-width: 636px) 100vw, 636px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Como puedes ver no es m\u00e1s que un l\u00edmite, y \u00a1ya sabemos calcular l\u00edmites! Sin embargo, para poder entender lo que representa, es necesario que recordemos cu\u00e1l es una<strong> recta tangente a una curva<\/strong> en un punto y cu\u00e1l es una <strong>recta secante a una curva <\/strong>en un punto. En las siguientes figuras te muestro una recta secante, la l\u00ednea verde, y una recta tangente, la l\u00ednea naranja. como recordar\u00e1s una secante corta a una curva en: mientras que una tangente toca a la curva en un solo punto<\/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-2023-08-04-a-las-9.43.34.png\" alt=\"\" class=\"wp-image-26945\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"875\" height=\"381\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.43.34.png\" alt=\"\" class=\"wp-image-26945\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.43.34.png 875w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.43.34-300x131.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.43.34-768x334.png 768w\" sizes=\"auto, (max-width: 875px) 100vw, 875px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Ahora bien, tambi\u00e9n es necesario recordar cu\u00e1l es la ecuaci\u00f3n de una recta.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Para la ecuaci\u00f3n de una recta necesitamos tener dos puntos por los cuales pasa la l\u00ednea recta:<\/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-2023-08-04-a-las-9.43.59.png\" alt=\"\" class=\"wp-image-26946\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"249\" height=\"80\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.43.59.png\" alt=\"\" class=\"wp-image-26946\" \/><\/noscript><\/figure>\n<\/div>\n\n\n<p class=\"wp-block-paragraph\">o bien necesitamos conocer la pendiente de la recta (m) y su intersecci\u00f3n con el eje de las x (b)<\/p>\n\n\n\n<p class=\"has-text-align-center has-medium-font-size wp-block-paragraph\"><strong>y = mx + b<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aqu\u00ed tienes dos videos que te pueden ayudar a recordar:<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Introducci\u00f3n a la ecuaci\u00f3n de la recta, fundamentos\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/GBSmycLgTeU?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Ecuaci\u00f3n de la recta conociendo dos puntos | Ejemplo 1\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/bo3JsAc9CbE?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Para unir estos elementos, revisemos cu\u00e1l es su relaci\u00f3n con la derivada. Observa las im\u00e1genes y mira c\u00f3mo la secante se va convirtiendo en una tangente cuando hacemos la <strong><em>h<\/em><\/strong> cada vez m\u00e1s peque\u00f1a, hasta que llega a cero:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><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-2023-08-04-a-las-9.45.14-853x1024.png\" alt=\"\" class=\"wp-image-26947\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"853\" height=\"1024\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.45.14-853x1024.png\" alt=\"\" class=\"wp-image-26947\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.45.14-853x1024.png 853w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.45.14-250x300.png 250w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.45.14-768x922.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.45.14.png 926w\" sizes=\"auto, (max-width: 853px) 100vw, 853px\" \/><\/noscript><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><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-2023-08-04-a-las-9.45.47-863x1024.png\" alt=\"\" class=\"wp-image-26949\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"863\" height=\"1024\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.45.47-863x1024.png\" alt=\"\" class=\"wp-image-26949\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.45.47-863x1024.png 863w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.45.47-253x300.png 253w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.45.47-768x911.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.45.47.png 928w\" sizes=\"auto, (max-width: 863px) 100vw, 863px\" \/><\/noscript><\/figure>\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-2023-08-04-a-las-9.46.19.png\" alt=\"\" class=\"wp-image-26950\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"931\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.46.19.png\" alt=\"\" class=\"wp-image-26950\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.46.19.png 936w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.46.19-300x298.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.46.19-150x150.png 150w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.46.19-768x764.png 768w\" sizes=\"auto, (max-width: 936px) 100vw, 936px\" \/><\/noscript><\/figure>\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-2023-08-04-a-las-9.48.30.png\" alt=\"\" class=\"wp-image-26951\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"929\" height=\"882\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.48.30.png\" alt=\"\" class=\"wp-image-26951\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.48.30.png 929w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.48.30-300x285.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.48.30-768x729.png 768w\" sizes=\"auto, (max-width: 929px) 100vw, 929px\" \/><\/noscript><\/figure>\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-2023-08-04-a-las-9.49.29.png\" alt=\"\" class=\"wp-image-26952\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"847\" height=\"195\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.49.29.png\" alt=\"\" class=\"wp-image-26952\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.49.29.png 847w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.49.29-300x69.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.49.29-768x177.png 768w\" sizes=\"auto, (max-width: 847px) 100vw, 847px\" \/><\/noscript><\/figure>\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-2023-08-04-a-las-9.50.12.png\" alt=\"\" class=\"wp-image-26953\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"930\" height=\"967\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.50.12.png\" alt=\"\" class=\"wp-image-26953\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.50.12.png 930w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.50.12-289x300.png 289w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.50.12-768x799.png 768w\" sizes=\"auto, (max-width: 930px) 100vw, 930px\" \/><\/noscript><\/figure>\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-2023-08-04-a-las-9.51.12.png\" alt=\"\" class=\"wp-image-26954\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"646\" height=\"466\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.51.12.png\" alt=\"\" class=\"wp-image-26954\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.51.12.png 646w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.51.12-300x216.png 300w\" sizes=\"auto, (max-width: 646px) 100vw, 646px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Si no recuerdas las funciones trigonom\u00e9tricas te dejo unos enlaces para que veas los videos y te acuerdes<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Veamos otras funciones y sus derivadas<\/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-2023-08-04-a-las-9.52.01.png\" alt=\"\" class=\"wp-image-26955\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"926\" height=\"587\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.52.01.png\" alt=\"\" class=\"wp-image-26955\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.52.01.png 926w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.52.01-300x190.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.52.01-768x487.png 768w\" sizes=\"auto, (max-width: 926px) 100vw, 926px\" \/><\/noscript><\/figure>\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-2023-08-04-a-las-9.52.47.png\" alt=\"\" class=\"wp-image-26956\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"779\" height=\"735\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.52.47.png\" alt=\"\" class=\"wp-image-26956\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.52.47.png 779w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.52.47-300x283.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.52.47-768x725.png 768w\" sizes=\"auto, (max-width: 779px) 100vw, 779px\" \/><\/noscript><\/figure>\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-2023-08-04-a-las-9.55.46.png\" alt=\"\" class=\"wp-image-26958\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"843\" height=\"372\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.55.46.png\" alt=\"\" class=\"wp-image-26958\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.55.46.png 843w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.55.46-300x132.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.55.46-768x339.png 768w\" sizes=\"auto, (max-width: 843px) 100vw, 843px\" \/><\/noscript><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Producto y divisi\u00f3n de funciones<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">No es muy com\u00fan encontrar solamente funciones como polinomios o que tengamos solamente senos o cosenos como elementos dentro de una funci\u00f3n, muchas veces encontramos una funci\u00f3n m\u00e1s compleja, que bien puede ser el producto de 2 o m\u00e1s funciones.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ahora veamos c\u00f3mo derivar el producto y divisi\u00f3n de funciones. Consideremos 2 funciones\u00a0f(x) \u00a0 y\u00a0 g(x), las cuales se encuentran generando una nueva funci\u00f3n mediante el producto o divisi\u00f3n de ellas.<\/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-2023-08-04-a-las-9.56.55.png\" alt=\"\" class=\"wp-image-26960\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"927\" height=\"824\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.56.55.png\" alt=\"\" class=\"wp-image-26960\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.56.55.png 927w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.56.55-300x267.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.56.55-768x683.png 768w\" sizes=\"auto, (max-width: 927px) 100vw, 927px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">En palabras dir\u00eda \u201cla derivada de un producto de funciones es igual a la derivada de la primera funci\u00f3n por la segunda menos la derivada de la segunda funci\u00f3n por la primera dividido entre la segunda funci\u00f3n al cuadrado\u201d.<\/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-2023-08-04-a-las-9.58.09.png\" alt=\"\" class=\"wp-image-26962\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"890\" height=\"969\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.58.09.png\" alt=\"\" class=\"wp-image-26962\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.58.09.png 890w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.58.09-276x300.png 276w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2023\/08\/Captura-de-pantalla-2023-08-04-a-las-9.58.09-768x836.png 768w\" sizes=\"auto, (max-width: 890px) 100vw, 890px\" \/><\/noscript><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"conclusion\">Conclusi\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Espero que te hayas aprendido el concepto de derivada, y que te hayas aprendido las f\u00f3rmulas, seguiremos aplic\u00e1ndolo. Aunque a\u00fan no hemos visto ejemplos de su uso, ten paciencia, pronto veremos ejemplos de aplicaci\u00f3n.<\/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 99-145 numeraci\u00f3n del libro<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Introducci\u00f3n Hemos llegado al tema m\u00e1s \u00fatil en el \u00e1rea de ingenier\u00eda, f\u00edsica, qu\u00edmica y dem\u00e1s ciencias exactas, las derivadas. No se trata de un proceso complicado, solo te pido que memorices las f\u00f3rmulas y que hagas muchas derivadas y ver\u00e1s,que despu\u00e9s de un rato se vuelven m\u00e1s f\u00e1ciles. La derivada se define a partir &#8230; <a title=\"Clase digital 5. Derivadas\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-5-derivadas\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 5. Derivadas\">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-26577","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\/26577","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=26577"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/26577\/revisions"}],"predecessor-version":[{"id":26963,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/26577\/revisions\/26963"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=26577"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=26577"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=26577"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}