{"id":4625,"date":"2022-01-14T21:01:13","date_gmt":"2022-01-14T21:01:13","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=4625"},"modified":"2022-02-08T18:59:28","modified_gmt":"2022-02-08T18:59:28","slug":"clase-digital-7-interpretacion-geometrica-de-la-derivada-recta-tangente-y-la-derivada-incremento-y-razon-de-cambio","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-7-interpretacion-geometrica-de-la-derivada-recta-tangente-y-la-derivada-incremento-y-razon-de-cambio\/","title":{"rendered":"Clase digital 7: Interpretacio\u0301n geome\u0301trica de la derivada"},"content":{"rendered":"\n\n\n<div class=\"wp-block-cover is-light\" style=\"min-height:284px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"has-background-dim-40 wp-block-cover__gradient-background has-background-dim\"><\/span><img decoding=\"async\" class=\"wp-block-cover__image-background wp-image-4770\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/937884.jpg\" style=\"object-position:68% 0%\" data-object-fit=\"cover\" data-object-position=\"68% 0%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1280\" height=\"853\" class=\"wp-block-cover__image-background wp-image-4770\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/937884.jpg\" style=\"object-position:68% 0%\" data-object-fit=\"cover\" data-object-position=\"68% 0%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/937884.jpg 1280w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/937884-300x200.jpg 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/937884-1024x682.jpg 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/937884-768x512.jpg 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/937884-272x182.jpg 272w\" sizes=\"auto, (max-width: 1280px) 100vw, 1280px\" \/><\/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\">Interpretaci\u00f3n geom\u00e9trica de la derivada<\/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\">\u00a1Hola!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Qu\u00e9 emoci\u00f3n volvernos a encontrar! Espero que sigas con ese mismo \u00edmpetu de la primera clase y contin\u00faes aprendiendo, por lo tanto te invito a esta s\u00e9ptima clase titulada INTERPRETACIO\u0301N GEOME\u0301TRICA DE LA DERIVADA del curso <strong>C\u00e1lculo Diferencial<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En esta clase, se analizar\u00e1n los problemas cl\u00e1sicos que dan origen al c\u00e1lculo infinitesimal, estos problemas comenzaron a plantearse en la \u00e9poca cl\u00e1sica de la antigua Grecia, pero no se encontraron m\u00e9todos sistem\u00e1ticos de resoluci\u00f3n si no hasta el siglo XVII por obras del ingl\u00e9s Issac Newton y el alem\u00e1n Gottfried Leibniz.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En lo correspondiente a las derivadas existen dos conceptos de tipo geom\u00e9trico que le dieron origen a: El problema de la tangente a una curva, el teorema de los extremos m\u00e1ximos y m\u00ednimos<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Espero que disfrutes esta sesi\u00f3n. \u00a1Mucho \u00e9xito!<\/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\" id=\"interpretacion-geometrica-de-la-derivada\">Interpretaci\u00f3n geom\u00e9trica de la derivada<\/h3>\n\n\n\n<div class=\"wp-block-image\"><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\/2022\/01\/y.png\" alt=\"\" class=\"wp-image-4776\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"838\" height=\"434\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/y.png\" alt=\"\" class=\"wp-image-4776\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/y.png 838w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/y-300x155.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/y-768x398.png 768w\" sizes=\"auto, (max-width: 838px) 100vw, 838px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Sea f una funci\u00f3n definida en un intervalo abierto I, que contiene al n\u00famero a y que adem\u00e1s existe el l\u00edmite<\/p>\n\n\n\n<div class=\"wp-block-image\"><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\/2022\/01\/ay.png\" alt=\"\" class=\"wp-image-4778\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"622\" height=\"115\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/ay.png\" alt=\"\" class=\"wp-image-4778\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/ay.png 622w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/ay-300x55.png 300w\" sizes=\"auto, (max-width: 622px) 100vw, 622px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><br>entonces, la recta que pasa por (a,f(a)) y tiene pendiente m es la recta tangente a la gr\u00e1fica de f en el punto (a,f(a)) y cuya ecuaci\u00f3n esta dada por <em>y=m(x-a)+f(a)<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ejemplo<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Encuentra la pendiente y la ecuaci\u00f3n de la recta tangente a la gr\u00e1fica de f(x)=x<sup>2<\/sup> en el punto P(2,4).<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo-1-1.png\" alt=\"\" class=\"wp-image-4781\" width=\"863\" height=\"490\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo-1-1.png\" alt=\"\" class=\"wp-image-4781\" width=\"863\" height=\"490\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo-1-1.png 722w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo-1-1-300x170.png 300w\" sizes=\"auto, (max-width: 863px) 100vw, 863px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo-2.png\" alt=\"\" class=\"wp-image-4782\" width=\"836\" height=\"944\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo-2.png\" alt=\"\" class=\"wp-image-4782\" width=\"836\" height=\"944\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo-2.png 660w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo-2-265x300.png 265w\" sizes=\"auto, (max-width: 836px) 100vw, 836px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/c2.png\" alt=\"\" class=\"wp-image-4784\" width=\"839\" height=\"382\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/c2.png\" alt=\"\" class=\"wp-image-4784\" width=\"839\" height=\"382\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/c2.png 655w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/c2-300x136.png 300w\" sizes=\"auto, (max-width: 839px) 100vw, 839px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"razon-de-cambio-promedio\">Raz\u00f3n de cambio promedio<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Supongamos que x y y son dos variables relacionadas, en las que el cambio en una influyen en un cambio en la otra, designemos como Dx y Dy los incrementos en dichas variables, la raz\u00f3n de cambio promedio es el cociente<\/p>\n\n\n\n<div class=\"wp-block-image\"><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\/2022\/01\/ay-2.png\" alt=\"\" class=\"wp-image-4788\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"237\" height=\"143\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/ay-2.png\" alt=\"\" class=\"wp-image-4788\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ejemplo<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Consideremos un cilindro de gas, el cual tiene dos medidores, uno de temperatura y otro de presi\u00f3n. Un d\u00eda caluroso se registran la temperatura y presi\u00f3n en distintos tiempos.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Cilindro.png\" alt=\"\" class=\"wp-image-4789\" width=\"859\" height=\"96\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Cilindro.png\" alt=\"\" class=\"wp-image-4789\" width=\"859\" height=\"96\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Cilindro.png 743w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Cilindro-300x33.png 300w\" sizes=\"auto, (max-width: 859px) 100vw, 859px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La raz\u00f3n de cambio promedio entre el incremento de temperatura y el incremento de tiempo en el intervalo de 6 a 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Definici\u00f3n de la derivada de una funci\u00f3n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sea f una funci\u00f3n definida en un intervalo abierto I que contiene al n\u00famero c. La derivada de f en c, denotada como f\u2019(c) est\u00e1 dada por:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/fc.png\" alt=\"\" class=\"wp-image-4790\" width=\"336\" height=\"124\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/fc.png\" alt=\"\" class=\"wp-image-4790\" width=\"336\" height=\"124\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/fc.png 325w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/fc-300x111.png 300w\" sizes=\"auto, (max-width: 336px) 100vw, 336px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ejemplo<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Encuentra f'(1)si f(x)=x<sup>3<\/sup>+2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Por definici\u00f3n<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Primer paso: <em>f(1)=(1)<sup>3<\/sup>+2=3<\/em><\/p>\n\n\n\n<h3 class=\"has-text-align-center wp-block-heading\" id=\"f-1-x-1-x-3-2-1-3-x-3-x2-x3-2-3-x-3-x2-x3-3\">f(1+\u2206x)=(1+\u2206x)<sup>3<\/sup>+2=1+3\u2206x+3\u2206x<sup>2<\/sup>+\u2206x<sup>3<\/sup>+2 =3\u2206x+3\u2206x<sup>2<\/sup>+\u2206x<sup>3<\/sup>+3<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Segundo paso<em><strong> <\/strong><\/em><\/p>\n\n\n\n<h3 class=\"has-text-align-center wp-block-heading\" id=\"f-1-x-f-1\">f(1+\u2206x)-f(1)<\/h3>\n\n\n\n<h3 class=\"has-text-align-center wp-block-heading\" id=\"f-1-x-f-1-3-x-3-x2-x3-3-3-3-x-3-x2-x3\">f(1+\u2206x)-f(1)=3\u2206x+3\u2206x<sup>2<\/sup>+\u2206x<sup>3<\/sup>+3-3 =3\u2206x+3\u2206x<sup>2<\/sup>+\u2206x<sup>3<\/sup><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Factorizando delta x<\/p>\n\n\n\n<h3 class=\"has-text-align-center wp-block-heading\" id=\"x-3-3-x-x2\">=\u2206x(3+3\u2206x+\u2206x<sup>2<\/sup>)<\/h3>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tercer-y-cuarto-paso.png\" alt=\"\" class=\"wp-image-4793\" width=\"919\" height=\"192\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tercer-y-cuarto-paso.png\" alt=\"\" class=\"wp-image-4793\" width=\"919\" height=\"192\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tercer-y-cuarto-paso.png 820w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tercer-y-cuarto-paso-300x63.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tercer-y-cuarto-paso-768x160.png 768w\" sizes=\"auto, (max-width: 919px) 100vw, 919px\" \/><\/noscript><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"la-derivada-como-una-funcion\">La derivada como una funci\u00f3n<\/h3>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/F-3.png\" alt=\"\" class=\"wp-image-4795\" width=\"246\" height=\"82\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/F-3.png\" alt=\"\" class=\"wp-image-4795\" width=\"246\" height=\"82\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">siempre y cuando el l\u00edmite exista.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ejemplo<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><br>Sea f(x)=x<sup>3<\/sup>+2 encontrar: la derivada y su dominio, f\u2019(-1) y la ecuaci\u00f3n de la recta tangente en c=-1, f\u2019(1) y la ecuaci\u00f3n de la recta tangente en c=1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Primer paso <strong>f(x+\u2206x)<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><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\/2022\/01\/F-4.png\" alt=\"\" class=\"wp-image-4796\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"690\" height=\"85\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/F-4.png\" alt=\"\" class=\"wp-image-4796\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/F-4.png 690w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/F-4-300x37.png 300w\" sizes=\"auto, (max-width: 690px) 100vw, 690px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Segundo paso <strong>f(x+\u2206x)-f(x)<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Segundo-paso.png\" alt=\"\" class=\"wp-image-4798\" width=\"551\" height=\"176\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Segundo-paso.png\" alt=\"\" class=\"wp-image-4798\" width=\"551\" height=\"176\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Segundo-paso.png 489w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Segundo-paso-300x96.png 300w\" sizes=\"auto, (max-width: 551px) 100vw, 551px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Factorizando delta x<\/p>\n\n\n\n<div class=\"wp-block-image\"><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\/2022\/01\/Segundo-paso-1.png\" alt=\"\" class=\"wp-image-4799\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"347\" height=\"107\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Segundo-paso-1.png\" alt=\"\" class=\"wp-image-4799\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Segundo-paso-1.png 347w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Segundo-paso-1-300x93.png 300w\" sizes=\"auto, (max-width: 347px) 100vw, 347px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><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\/2022\/01\/Tercer-paso.png\" alt=\"\" class=\"wp-image-4800\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"678\" height=\"756\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tercer-paso.png\" alt=\"\" class=\"wp-image-4800\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tercer-paso.png 678w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tercer-paso-269x300.png 269w\" sizes=\"auto, (max-width: 678px) 100vw, 678px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><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\/2022\/01\/Tercer-paso-2.png\" alt=\"\" class=\"wp-image-4801\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"677\" height=\"250\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tercer-paso-2.png\" alt=\"\" class=\"wp-image-4801\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tercer-paso-2.png 677w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Tercer-paso-2-300x111.png 300w\" sizes=\"auto, (max-width: 677px) 100vw, 677px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"la-diferencial\">La diferencial<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Supongamos una funci\u00f3n f cuya derivada en c existe, entonces la ecuaci\u00f3n de la recta tangente a la gr\u00e1fica de f en el punto (c,f(c)) viene dada por la ecuaci\u00f3n y=f'(x)(x-c)+f(x).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Si <strong>y=f(x)<\/strong> es una funci\u00f3n derivable en un intervalo abierto que contiene a x. la diferencial de <strong>x(dx)<\/strong> es cualquier n\u00famero real diferente de cero. La diferencial de<strong> y(dy)<\/strong> se define como <strong>dy=f'(x)<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"calculo-de-derivadas\">C\u00e1lculo de derivadas<\/h3>\n\n\n\n<h5 class=\"wp-block-heading\" id=\"reglas-basicas-de-la-derivacion\">Reglas b\u00e1sicas de la derivaci\u00f3n<\/h5>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Derivada de una constante<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aplicando la definici\u00f3n de derivada obtenga la derivada de una funci\u00f3n f(x)=C, donde C, es una constante<\/p>\n\n\n\n<div class=\"wp-block-image\"><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\/2022\/01\/Derivada-de-una-cosntante.png\" alt=\"\" class=\"wp-image-4803\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"444\" height=\"314\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Derivada-de-una-cosntante.png\" alt=\"\" class=\"wp-image-4803\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Derivada-de-una-cosntante.png 444w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Derivada-de-una-cosntante-300x212.png 300w\" sizes=\"auto, (max-width: 444px) 100vw, 444px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Derivada de una potencia<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Aplicando la definici\u00f3n de derivada obtenga la derivada de una funci\u00f3n f(x)=x<sup>2<\/sup><\/p>\n\n\n\n<div class=\"wp-block-image\"><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\/2022\/01\/Ejemplo-de-una-potencia.png\" alt=\"\" class=\"wp-image-4804\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"713\" height=\"604\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo-de-una-potencia.png\" alt=\"\" class=\"wp-image-4804\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo-de-una-potencia.png 713w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Ejemplo-de-una-potencia-300x254.png 300w\" sizes=\"auto, (max-width: 713px) 100vw, 713px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Derivada de un m\u00faltiplo de una funci\u00f3n<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><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\/2022\/01\/CF.png\" alt=\"\" class=\"wp-image-4805\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"730\" height=\"616\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CF.png\" alt=\"\" class=\"wp-image-4805\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CF.png 730w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/CF-300x253.png 300w\" sizes=\"auto, (max-width: 730px) 100vw, 730px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Derivada de un cociente de funciones<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><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\/2022\/01\/Derivada-de-un-cociente-de-funciones.png\" alt=\"\" class=\"wp-image-4806\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"728\" height=\"731\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Derivada-de-un-cociente-de-funciones.png\" alt=\"\" class=\"wp-image-4806\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Derivada-de-un-cociente-de-funciones.png 728w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Derivada-de-un-cociente-de-funciones-300x300.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Derivada-de-un-cociente-de-funciones-150x150.png 150w\" sizes=\"auto, (max-width: 728px) 100vw, 728px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Derivadas de las funciones trigonom\u00e9tricas<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><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\/2022\/01\/lim-4.png\" alt=\"\" class=\"wp-image-4807\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"694\" height=\"771\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim-4.png\" alt=\"\" class=\"wp-image-4807\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim-4.png 694w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/lim-4-270x300.png 270w\" sizes=\"auto, (max-width: 694px) 100vw, 694px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Graficas-1.png\" alt=\"\" class=\"wp-image-4808\" width=\"886\" height=\"866\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Graficas-1.png\" alt=\"\" class=\"wp-image-4808\" width=\"886\" height=\"866\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Graficas-1.png 703w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/01\/Graficas-1-300x294.png 300w\" sizes=\"auto, (max-width: 886px) 100vw, 886px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"conclusion\">Conclusi\u00f3n <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">En resumen, el an\u00e1lisis de la derivada de una funci\u00f3n es en s\u00ed misma una funci\u00f3n que proporciona la pendiente de una recta tangente. La derivada no es, sin embargo, una ecuaci\u00f3n de una recta tangente. Recuerde que f\u2019(x) debe evaluarse en xo antes de usarla en la forma punto-pendiente. Si es diferenciable en xo, entonces la ecuaci\u00f3n de la recta tangente en (xo, yo) es y-yo=f\u2019(xo)(x-xo).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">La derivada f\u2019(x) tambi\u00e9n es la raz\u00f3n de cambio instant\u00e1neo de la funci\u00f3n y=f(x) con respecto a la variable x.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Has concluido la clase del curso! \u00a1Muchas felicidades!. No olvides realizar la tarea asignada para la plena conclusi\u00f3n de la clase. Espero encontrarte nuevamente, \u00a1hasta pronto!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introducci\u00f3n \u00a1Hola! \u00a1Qu\u00e9 emoci\u00f3n volvernos a encontrar! Espero que sigas con ese mismo \u00edmpetu de la primera clase y contin\u00faes aprendiendo, por lo tanto te invito a esta s\u00e9ptima clase titulada INTERPRETACIO\u0301N GEOME\u0301TRICA DE LA DERIVADA del curso C\u00e1lculo Diferencial. En esta clase, se analizar\u00e1n los problemas cl\u00e1sicos que dan origen al c\u00e1lculo infinitesimal, estos &#8230; <a title=\"Clase digital 7: Interpretacio\u0301n geome\u0301trica de la derivada\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-7-interpretacion-geometrica-de-la-derivada-recta-tangente-y-la-derivada-incremento-y-razon-de-cambio\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 7: Interpretacio\u0301n geome\u0301trica de la derivada\">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":[10,12],"tags":[41,149,44],"class_list":["post-4625","post","type-post","status-publish","format-standard","hentry","category-ingenieria-civil","category-uda-calculo-diferencial","tag-clase-digital","tag-marcela-guadalupe-tellez-martinez","tag-neli04036"],"acf":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/4625","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=4625"}],"version-history":[{"count":4,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/4625\/revisions"}],"predecessor-version":[{"id":6952,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/4625\/revisions\/6952"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=4625"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=4625"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=4625"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}