{"id":1055,"date":"2024-02-19T13:16:38","date_gmt":"2024-02-19T13:16:38","guid":{"rendered":"https:\/\/wuolah.com\/blog\/?p=1055"},"modified":"2024-02-20T13:38:58","modified_gmt":"2024-02-20T13:38:58","slug":"tabla-de-derivadas","status":"publish","type":"post","link":"https:\/\/wuolah.com\/blog\/tabla-de-derivadas\/","title":{"rendered":"Tabla de Derivadas: Todas las formulas"},"content":{"rendered":"\n<p>La tabla de derivadas es una colecci\u00f3n de f\u00f3rmulas que muestran c\u00f3mo derivar una amplia gama de funciones matem\u00e1ticas, desde las m\u00e1s simples hasta las m\u00e1s complejas. <\/p>\n\n\n\n<p>Su prop\u00f3sito es doble: por un lado, sirve como una herramienta de referencia r\u00e1pida para resolver problemas de c\u00e1lculo diferencial, y por otro, ayuda a los estudiantes a internalizar los patrones y principios subyacentes en la operaci\u00f3n de derivaci\u00f3n.<\/p>\n\n\n\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 ez-toc-wrap-left counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Tabla de contenidos<\/p>\n<span class=\"ez-toc-title-toggle\"><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/wuolah.com\/blog\/tabla-de-derivadas\/#Tabla_de_Derivadas_Mas_Comunes\" >Tabla de Derivadas M\u00e1s Comunes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/wuolah.com\/blog\/tabla-de-derivadas\/#Tabla_de_Derivadas_Inmediatas\" >Tabla de Derivadas Inmediatas<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/wuolah.com\/blog\/tabla-de-derivadas\/#Tabla_de_Derivadas_Compuestas\" >Tabla de Derivadas Compuestas<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/wuolah.com\/blog\/tabla-de-derivadas\/#Tabla_de_Derivadas_de_Funciones_Especificas\" >Tabla de Derivadas de Funciones Espec\u00edficas<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"wp-block-heading\" id=\"h-tabla-de-derivadas-mas-comunes\"><span class=\"ez-toc-section\" id=\"Tabla_de_Derivadas_Mas_Comunes\"><\/span>Tabla de Derivadas M\u00e1s Comunes<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Aqui tienes la tabla de derivadas mas comunes. Con las funciones mas b\u00e1sicas y sus derivadas:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Funci\u00f3n <em>f<\/em>(<em>x<\/em>)<\/th><th>Derivada f\u2032(<em>x<\/em>)<\/th><th>Observaciones<\/th><\/tr><\/thead><tbody><tr><td><em>c<\/em><\/td><td>0<\/td><td><em>c<\/em> es una constante<\/td><\/tr><tr><td><em>x<sup>n<\/sup><\/em><\/td><td><em>nx<\/em><sup><em>n<\/em>\u22121<\/sup><\/td><td><em>n<\/em> es un n\u00famero real<\/td><\/tr><tr><td><em>e<sup>x<\/sup><\/em><\/td><td><em>e<sup>x<\/sup><\/em><\/td><td>La base del logaritmo natural <em>e<\/em> es \u00fanica por esta propiedad<\/td><\/tr><tr><td>log(<em>x<\/em>)<\/td><td>1\/<em>x<\/em><\/td><td>Logaritmo natural de <em>x<\/em><\/td><\/tr><tr><td>sin(<em>x<\/em>)<\/td><td>cos(<em>x<\/em>)<\/td><td>Funci\u00f3n trigonom\u00e9trica<\/td><\/tr><tr><td>cos(<em>x<\/em>)<\/td><td>\u2212sin(<em>x<\/em>)<\/td><td>Funci\u00f3n trigonom\u00e9trica<\/td><\/tr><tr><td>tan(<em>x<\/em>)<\/td><td>sec<sup>2<\/sup>(<em>x<\/em>)<\/td><td>Funci\u00f3n trigonom\u00e9trica<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-tabla-de-derivadas-inmediatas\"><span class=\"ez-toc-section\" id=\"Tabla_de_Derivadas_Inmediatas\"><\/span>Tabla de Derivadas Inmediatas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Las derivadas inmediatas son aquellas que podemos calcular directamente a partir de la funci\u00f3n original sin necesidad de simplificaciones adicionales. La tabla de las derivadas inmediatas es la siguiente:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Funci\u00f3n <em>f<\/em>(<em>x<\/em>)<\/th><th>Derivada <em>f<\/em>\u2032(<em>x<\/em>)<\/th><th>Observaciones<\/th><\/tr><\/thead><tbody><tr><td><em>c<\/em><\/td><td>0<\/td><td><em>c<\/em> es una constante.<\/td><\/tr><tr><td><em>x<\/em><\/td><td>1<\/td><td>Derivada de una variable respecto a s\u00ed misma.<\/td><\/tr><tr><td><em>e<sup>x<\/sup><\/em><\/td><td><em>e<sup>x<\/sup><\/em><\/td><td>La funci\u00f3n exponencial mantiene su forma.<\/td><\/tr><tr><td>ln(<em>x<\/em>)<\/td><td>1\/<em>x<\/em><\/td><td>Logaritmo natural, inverso de <em>e<sup>x<\/sup><\/em>.<\/td><\/tr><tr><td>sin(<em>x<\/em>)<\/td><td>cos(<em>x<\/em>)<\/td><td>Funci\u00f3n trigonom\u00e9trica b\u00e1sica.<\/td><\/tr><tr><td>cos(<em>x<\/em>)<\/td><td>\u2212sin(<em>x<\/em>)<\/td><td>Funci\u00f3n trigonom\u00e9trica b\u00e1sica.<\/td><\/tr><tr><td>tan(<em>x<\/em>)<\/td><td>sec<sup>2<\/sup>(<em>x<\/em>)<\/td><td>Derivada directa de la tangente.<\/td><\/tr><tr><td>sec(<em>x<\/em>)<\/td><td>sec(<em>x<\/em>)tan(<em>x<\/em>)<\/td><td>Funci\u00f3n trigonom\u00e9trica.<\/td><\/tr><tr><td>csc(<em>x<\/em>)<\/td><td>\u2212csc(<em>x<\/em>)cot(<em>x<\/em>)<\/td><td>Funci\u00f3n trigonom\u00e9trica.<\/td><\/tr><tr><td>cot(<em>x<\/em>)<\/td><td>\u2212csc2(<em>x<\/em>)<\/td><td>Funci\u00f3n trigonom\u00e9trica.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-tabla-de-derivadas-compuestas\"><span class=\"ez-toc-section\" id=\"Tabla_de_Derivadas_Compuestas\"><\/span>Tabla de Derivadas Compuestas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>La derivaci\u00f3n de funciones compuestas es un concepto crucial en el c\u00e1lculo diferencial, que se ocupa de las tasas de cambio de funciones que est\u00e1n compuestas por otras funciones. Este proceso se lleva a cabo utilizando la regla de la cadena, que nos permite diferenciar una composici\u00f3n de funciones de manera sistem\u00e1tica. La regla de la cadena establece que si tenemos dos funciones <em>u(x)<\/em> y <em>v(u)<\/em>, y queremos encontrar la derivada de la composici\u00f3n <em>v(u(x))<\/em>, entonces la derivada es el producto de la derivada de <em>v<\/em> respecto a <em>u<\/em> y la derivada de <em>u<\/em> respecto a <em>x<\/em>. Es decir, <em>(v(u(x)))\u2032=v\u2032(u(x))*u\u2032(x)<\/em>.<\/p>\n\n\n\n<p>A continuaci\u00f3n, presentamos una tabla de derivadas compuestas com\u00fanmente encontradas, ilustrando c\u00f3mo se aplica la regla de la cadena en diferentes contextos:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Funci\u00f3n Compuesta <em>f<\/em>(<em>x<\/em>)<\/th><th>Derivada <em>f<\/em>\u2032(<em>x<\/em>) con Regla de la Cadena<\/th><th>Observaciones<\/th><\/tr><\/thead><tbody><tr><td><em>e<\/em><sup><em>g<\/em>(<em>x<\/em>)<\/sup><\/td><td><em>e<\/em><sup><em>g<\/em>(<em>x<\/em>)<\/sup><em>g<\/em>\u2032(<em>x<\/em>)<\/td><td>Aplicaci\u00f3n de la regla de la cadena a la funci\u00f3n exponencial.<\/td><\/tr><tr><td>ln(<em>g<\/em>(<em>x<\/em>))<\/td><td>[1\/<em>g<\/em>(<em>x<\/em>)]\u200b*<em>g<\/em>\u2032(<em>x<\/em>)<\/td><td>Aplicaci\u00f3n a la funci\u00f3n logar\u00edtmica natural.<\/td><\/tr><tr><td>sin(<em>g<\/em>(<em>x<\/em>))<\/td><td>cos(<em>g<\/em>(<em>x<\/em>))<em>g<\/em>\u2032(<em>x<\/em>)<\/td><td>Derivada de la composici\u00f3n con la funci\u00f3n seno.<\/td><\/tr><tr><td>cos(<em>g<\/em>(<em>x<\/em>))<\/td><td>\u2212sin(<em>g<\/em>(<em>x<\/em>))<em>g<\/em>\u2032(<em>x<\/em>)<\/td><td>Derivada de la composici\u00f3n con la funci\u00f3n coseno.<\/td><\/tr><tr><td><em>g<\/em>(<em>x<\/em>)<em><sup>n<\/sup><\/em><\/td><td><em>n<\/em>*<em>g<\/em>(<em>x<\/em>)<sup><em>n<\/em>\u22121<\/sup><em>g<\/em>\u2032(<em>x<\/em>)<\/td><td>Aplicaci\u00f3n de la regla de potencia a una funci\u00f3n compuesta.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-tabla-de-derivadas-de-funciones-especificas\"><span class=\"ez-toc-section\" id=\"Tabla_de_Derivadas_de_Funciones_Especificas\"><\/span>Tabla de Derivadas de Funciones Espec\u00edficas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>En el c\u00e1lculo diferencial, adem\u00e1s de las funciones b\u00e1sicas y sus composiciones, existen funciones espec\u00edficas cuya diferenciaci\u00f3n requiere un enfoque particular. Estas funciones incluyen las funciones trigonom\u00e9tricas inversas, las funciones hiperb\u00f3licas y sus inversas, entre otras.<\/p>\n\n\n\n<p>A continuaci\u00f3n, se presenta una tabla que resume las derivadas de algunas funciones espec\u00edficas, proporcionando una referencia r\u00e1pida para su c\u00e1lculo:<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"880\" height=\"443\" src=\"https:\/\/wuolah.com\/blog\/wp-content\/uploads\/sites\/2\/2024\/02\/tabla-de-derivadas-de-funciones-especificas.png\" alt=\"\" class=\"wp-image-1057\" srcset=\"https:\/\/wuolah.com\/blog\/wp-content\/uploads\/sites\/2\/2024\/02\/tabla-de-derivadas-de-funciones-especificas.png 880w, https:\/\/wuolah.com\/blog\/wp-content\/uploads\/sites\/2\/2024\/02\/tabla-de-derivadas-de-funciones-especificas-300x151.png 300w, https:\/\/wuolah.com\/blog\/wp-content\/uploads\/sites\/2\/2024\/02\/tabla-de-derivadas-de-funciones-especificas-768x387.png 768w, https:\/\/wuolah.com\/blog\/wp-content\/uploads\/sites\/2\/2024\/02\/tabla-de-derivadas-de-funciones-especificas-705x355.png 705w\" sizes=\"(max-width: 880px) 100vw, 880px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>La tabla de derivadas es una colecci\u00f3n de f\u00f3rmulas que muestran c\u00f3mo derivar una amplia gama de funciones matem\u00e1ticas, desde las m\u00e1s simples hasta las m\u00e1s complejas. Su prop\u00f3sito es doble: por un lado, sirve como una herramienta de referencia r\u00e1pida para resolver problemas de c\u00e1lculo diferencial, y por otro, ayuda a los estudiantes a [&hellip;]<\/p>\n","protected":false},"author":4,"featured_media":1058,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"class_list":["post-1055","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematicas"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.1 (Yoast SEO v25.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Tabla de Derivadas: Todas las formulas - Blog de Educaci\u00f3n - Wuolah<\/title>\n<meta name=\"description\" content=\"La tabla de derivadas es un recurso que facilita la compresi\u00f3n y aplicaci\u00f3n de este tipo de operaciones. 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