{"id":8265,"date":"2026-06-29T13:29:32","date_gmt":"2026-06-29T19:29:32","guid":{"rendered":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/?page_id=8265"},"modified":"2026-07-01T10:42:13","modified_gmt":"2026-07-01T16:42:13","slug":"derivacion","status":"publish","type":"page","link":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/derivacion\/","title":{"rendered":"Derivaci\u00f3n"},"content":{"rendered":"\n<p>La derivaci\u00f3n num\u00e9rica consiste en diferenciar la f\u00f3rmula de un polinomio interpolante con m\u00ednimos cuadrados, y del criterio de ajuste exacto. <\/p>\n\n\n\n<p>Tambi\u00e9n se han desarrollado formulas de derivaci\u00f3n utilizando el polinomio de interpolaci\u00f3n de Lagrange de segundo orden.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"751\" height=\"81\" src=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/06\/imagen.png\" alt=\"\" class=\"wp-image-8266\" srcset=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/06\/imagen.png 751w, https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/06\/imagen-300x32.png 300w\" sizes=\"(max-width: 751px) 100vw, 751px\" \/><\/figure>\n\n\n\n<p>donde t es el valor en el que se quiere estimar la derivada.<\/p>\n\n\n\n<p>Puede utilizarse para estimar derivadas en cualquier lugar del intervalo definido por tres puntos.<\/p>\n\n\n\n<h2>Ejemplo<\/h2>\n\n\n\n<p>Partiendo de la siguiente tabla, hallar la derivada en el punto t = 2<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>x<\/td><td>y = x exp(x)<\/td><\/tr><tr><td>1.9<\/td><td>12.7032<\/td><\/tr><tr><td>2.0<\/td><td>14.7781<\/td><\/tr><tr><td>2.1<\/td><td>17.1489<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Sustituyendo en la f\u00f3rmula<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"881\" height=\"135\" src=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/06\/imagen-1.png\" alt=\"\" class=\"wp-image-8267\" srcset=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/06\/imagen-1.png 881w, https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/06\/imagen-1-300x46.png 300w, https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/06\/imagen-1-768x118.png 768w\" sizes=\"(max-width: 881px) 100vw, 881px\" \/><\/figure>\n\n\n\n<p>La funci\u00f3n y la derivada de la funci\u00f3n son <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"209\" height=\"86\" src=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/07\/imagen.png\" alt=\"\" class=\"wp-image-8271\" \/><\/figure>\n\n\n\n<p>Sustituyendo para x = 2<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"382\" height=\"22\" src=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/07\/image.png\" alt=\"\" class=\"wp-image-8272\" srcset=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/07\/image.png 382w, https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/07\/image-300x17.png 300w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><\/figure>\n\n\n\n<p>Comparado con el valor estimado hay un ligero error de % error = 0.28<\/p>\n\n\n\n<h2 class=\"has-text-align-center\">Aproximaci\u00f3n a la derivada por derivadas finitas<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"369\" height=\"368\" src=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/07\/imagen-1.png\" alt=\"\" class=\"wp-image-8275\" srcset=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/07\/imagen-1.png 369w, https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/07\/imagen-1-300x300.png 300w, https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/07\/imagen-1-150x150.png 150w\" sizes=\"(max-width: 369px) 100vw, 369px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"805\" height=\"586\" src=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/07\/imagen-2.png\" alt=\"\" class=\"wp-image-8276\" srcset=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/07\/imagen-2.png 805w, https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/07\/imagen-2-300x218.png 300w, https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/07\/imagen-2-768x559.png 768w\" sizes=\"(max-width: 805px) 100vw, 805px\" \/><\/figure>\n\n\n\n<p>C\u00e1lculos con Excel<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" loading=\"lazy\" width=\"604\" height=\"156\" src=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/07\/imagen-3.png\" alt=\"\" class=\"wp-image-8277\" srcset=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/07\/imagen-3.png 604w, https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-content\/uploads\/sites\/89\/2026\/07\/imagen-3-300x77.png 300w\" sizes=\"(max-width: 604px) 100vw, 604px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>La derivaci\u00f3n num\u00e9rica consiste en diferenciar la f\u00f3rmula de un polinomio interpolante con m\u00ednimos cuadrados, y del criterio de ajuste exacto. Tambi\u00e9n se han desarrollado formulas de derivaci\u00f3n utilizando el polinomio de interpolaci\u00f3n de Lagrange de segundo orden. donde t es el valor en el que se quiere estimar la derivada. Puede utilizarse para estimar &hellip; <a href=\"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/derivacion\/\" class=\"more-link\">Contin\u00faa leyendo <span class=\"screen-reader-text\">Derivaci\u00f3n<\/span><\/a><\/p>\n","protected":false},"author":123458,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_bbp_topic_count":0,"_bbp_reply_count":0,"_bbp_total_topic_count":0,"_bbp_total_reply_count":0,"_bbp_voice_count":0,"_bbp_anonymous_reply_count":0,"_bbp_topic_count_hidden":0,"_bbp_reply_count_hidden":0,"_bbp_forum_subforum_count":0},"_links":{"self":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/8265"}],"collection":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/users\/123458"}],"replies":[{"embeddable":true,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/comments?post=8265"}],"version-history":[{"count":4,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/8265\/revisions"}],"predecessor-version":[{"id":8278,"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/pages\/8265\/revisions\/8278"}],"wp:attachment":[{"href":"https:\/\/blogceta.zaragoza.unam.mx\/mnumericos\/wp-json\/wp\/v2\/media?parent=8265"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}