[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-68189-es":3,"doc-seo-68189-110":31,"detail-sidebar-cat-0-es-110":93},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},68189,13056703019404,"Miles","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",38,"Examen","Derivadas - Tabla de Derivadas y Ejercicios con Soluciones","Guía escolar de Matemáticas dedicada al cálculo diferencial, centrada en una tabla de derivadas y en la aplicación a una amplia colección de funciones. Incluye reglas básicas para potencias, sumas, productos y cocientes, así como derivadas de funciones trigonométricas, exponenciales y logarítmicas, además de derivadas de funciones compuestas. El documento presenta una sección de ejercicios con expresiones variadas y otra de “soluciones sin simplificar”, mostrando el proceso derivativo paso a paso.","Departamento de Matemáticas I. E.S. Arroyo de la Miel  \nDERIVADAS  \n\n| TABLA DE DERIVADAS |  |\n| --- | --- |\n| y = C | y ′ = 0 |\n| y = f(x)n | y´=nf(x)n-1f´(x) |\n| y = f(x) ± g(x) | y ′ = f ′(x) ± g ′(x) |\n| y = c . f(x) | y ′ = c . f ′(x) |\n| y = f(x) . g(x) | y = f ′(x) . g(x) + g ′(x) . f(x) |\n| y =  f(x)\u003Cbr>g(x) | y = ~~ ~~f~~ ~~′(x)~~ ~~.~~ ~~g(x)~~ ~~-~~ ~~g2′(x)~~ ~~.~~ ~~f(x)\u003Cbr>g(x ) |\n| y = nf(x) | y ′ = 1 . f ′(x) n n f(x )n-1 |\n| y = L f(x) | y ′ = ~~ ~~f~~ ~~1(x) . f ′(x) |\n| y = ef(x) | y = ef(x) . f ′(x) |\n| y = af(x) | y ′ = af(x) . f ′(x) . L a |\n| y = sen f(x) | y ′ = cos f(x) . f ′(x) |\n| y = cos f(x) | y ′ = -sen f(x) . f ′(x) |\n| y = tg f(x) | y ′ = ~~ ~~cos21f(x) . f ′(x) |\n| y = cotg f(x) | y ′ = ~~ ~~sen1f(x) . f ′(x) |\n| y = arc sen f(x) | y ′ = 1 . f ′(x)\u003Cbr>  1 - f(x )2 |\n| y = arc cos f(x) | y ′ = -1 . f ′(x)\u003Cbr>  1 - f(x )2 |\n| y = arc tg f(x) | y ′ = ~~ ~~1~~ ~~+~~ ~~1f(x~~ ~~)2~~ ~~ . f ′(x) |\n| y = arc cotg f(x) | y ′ = ~~ ~~1~~ ~~+~~ ~~-f1(x~~ ~~)2~~ ~~ . f ′(x) |\n\nDepartamento de Matemáticas I. E.S. Arroyo de la Miel  \n1. y = 5x6-3x5+3x3-2 2. y = x-4+2x-3+x-4  \n3. y = 3 x10 + 2 ~~ ~~ + 3  4. y =  3 . x3 - π . x +  3 x  \n5. y = 4 senx-3 cosx 6. y = 2  + 2 + x5 x  \n7. y = 4x3 + 2x3-x3 + 4 8. y =  π . cos x - 3  2  \n9. y = cos(3x) 10. y = cos2(x3)  \n11. y = sen (3x2-2x) 12. y = cos(x2)  \n13. y = sen3(2x2) 14. y = cos4(3x4)  \n15. y = 3 sen2(2x-3) 16. y = cos5(3x2)  \n17. y = cos (senx) 18. y = cos2(sen(3x))  \n19. y = 3 cos2 x 20. y = 3 cos2 ( x2 )  \n21. y =  x2-3x 22. y = 3 ( x2-3x )2  \n23. y = ( 2  x - 3x )3 24. y = 3 sen2 x  \n25. y = 5 sen(3x) 26. y =  3x-senx  \n27. y = ( 3 x2 -  1-x2 )3 28. y = sen (  3 x2-5x )  \n29. y =  sen3 x + (x-1 )3 30. y = cos3 ( x2-3 x )  \n31. y = ~~ ~~x5~~ ~~ 32. y = ~~ ~~5x  \n33. y = ~~ ~~x4~~ ~~4-3x~~ ~~ 34. y = ~~ ~~x3x-3  \n35. y = ~~ ~~(~~ ~~x4-3x3~~ ~~)2~~ ~~ 36. y = ~~ ~~(x3-1x)3  \n37. y = x2  38. y =  3xx2-1 x  \n39. y =  40. y = x  \n x  3 x  \nDepartamento de Matemáticas I. E.S. Arroyo de la Miel  \n41. y = 3 3 x2-senx 42. y = l n (3x-1)  \n43. y = l n ( x2-3x) 44. y = l n  x-2  \n45. y = log2 (3 x2 ) 46. y = ex2  \n47. y = 2x 48. y = ex2-2x  \n49. y = 3sen x 50. y = tg ( x3 )  \n51. y = 3 ex2-3x 52. y =  ecosx  \n53. y = 3 tg 2 x 54. y = ( x2-1) . (x-1)  \n55. y = x2 . l n x 56. y = ex2 . cos x  \n57. y = x4 . e3 x 58. y = ex4-3x2 . sen x  \n59. y = l n x2 . esen x 60. y = 1  \nl n  x  \n61. y = 􀂨􀂧􀂩 xx22~~ ~~+-31 􀂷􀂹􀂸3 62. y = l n x . ex2-senx  \n63. y = ( cos2 3x - sen3 x ) . ex3 64. y = 􀂨􀂧􀂩 l~~ ~~nx~~ ~~3-x~~ ~~22 􀂷􀂹􀂸2  \n65. y = ~~ ~~l~~ ~~n3xx~~ ~~ 66. y = ~~ ~~exx2+-lsnenxx  \n67. y = l n 􀂨􀂧􀂩 senex~~ ~~x 􀂷􀂹􀂸 68. y =  sexn-x1   \n69. y = ~~ ~~3~~ ~~x4-22xx2-3x-2~~ ~~ 70. y = ( sen ( e3x ) )2 . cos x  \n71. y = arctg ( x2 ) 72. y = arcsen x3  \n73. y = l n (sec x) 74. y = arctg (l n x)  \n75. y = arcsen x . ecosx 76. y = arctg ( e3x )  \nDepartamento de Matemáticas I. E.S. Arroyo de la Miel  \n77. y = l n 􀂧􀂨􀂩 tgxe 3 x 2 􀂷􀂹􀂸 78. y = arcsen 􀂨􀂧􀂩 x+e x 1 􀂷  \n􀂸  \n􀂹  \n79. y = l n ( arctg(5x) ) 80. y = arctg 3  \nx  \n81. y = 5 arctg 2 (senx) 82. y = 3arctg ( x2 )  \n83. y = arcsen 3x-2) 84. y = sen x - tg xx 4x-3  \n85. y = xsenx 86. y = (sen x )x2  \n87. y = ( cos x )x3-x 88. y = 4arctg (l n x)  \n89. y = l n 􀂨􀂧􀂩 x22 􀂷􀂹􀂸 3 90. y = 􀂨􀂧􀂩 se 3xenx 􀂷􀂹􀂸x2  \n91. y = 10 se3xn-xco-e~~ ~~xsx 􀂷􀂹􀂸 92. y = cos 􀂨􀂧􀂩 setgn(l xn x) 􀂷􀂹􀂸  \n93. y = ~~ ~~xcosx~~ ~~3~~ ~~ 94. y = cos2 (4 ex ) . l n 􀂧􀂨 tgx2 􀂷􀂸(l n x ) 􀂩 3x 􀂹  \n95. y = 3 sen2 ( ex )  96. y = el nc(coossxx)  \n arctg (cosx)  5  \n97. y =  \n99. y =  \ncos( ex ) . xtgx  \ne  \narctg ex . cos xl n (x2-x)  \n98. y = ( tg ( ex ) + x2 )x  \n100. y = ocsosx  sen ( e )  \nSOLUCIONES SIN SIMPLIFICAR  \n1. y ′ = 30 x5 - 15 x4 + 9 x2 2. y ′ = -4 x-5 - 6 x-4 + 1  \n3. y ′ = 30 x9 + 1 - 32 4. y ′ = 3 3 . x2 - π x x  \nDepartamento de Matemáticas I. E.S. Arroyo de la Miel  \n5. y ′ = 4 cos x + 3 sen x 6. y ′ = 1 - ~~ ~~22 + 5 x4  \nx x  \n7. y ′ = 15 x2 8. y ′ = - ~~ ~~π sen x - 3  \n2 2  x  \n9. y ′ = -3 sen(3x) 10. y ′ = -2 cos( x3 ) . sen( x3 ) . 3 x2 11. y ′ = cos (3 x2-2x) .","cbCaiovdrlxnp6gm","https://ap.wps.com/l/cbCaiovdrlxnp6gm","pdf",1112567,6,1,10,"Spanish","es",110,"# Tabla de derivadas\n## Reglas de derivación\n## Funciones trigonométricas, exponenciales y logarítmicas\n# Ejercicios de derivación\n## Expresiones de funciones\n# Soluciones sin simplificar","[{\"question\":\"¿Qué tipos de reglas de derivación se incluyen en la tabla?\",\"answer\":\"Se incluyen reglas para constantes, potencias, sumas/diferencias, productos y funciones del tipo c·f(x) y f(x)·g(x), además de funciones compuestas.\"},{\"question\":\"¿La guía incluye derivadas de funciones trigonométricas?\",\"answer\":\"Sí. Contiene derivadas relacionadas con sen, cos, tg, cotg y arcos (arc sen, arc cos, arc tg, arc cotg), aplicadas también a argumentos compuestos.\"},{\"question\":\"¿Qué es la sección “Soluciones sin simplificar” y para qué sirve?\",\"answer\":\"Reúne el resultado derivado para los ejercicios manteniendo el desarrollo sin realizar simplificaciones, con el objetivo de practicar el procedimiento paso a paso.\"}]","Derivadas - Tabla de Derivadas y Ejercicios con Soluciones | PDF",1784003267,15,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":88,"head_meta":90,"extra_data":92,"updated_unix":29},"derivatives-derivative-table-and-exercises-with-solutions","",{"@graph":37,"@context":87},[38,55,70],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,52],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/es/document/","Document",2,{"item":50,"name":12,"@type":44,"position":51},"https://docshare.wps.com/es/document/examen/",3,{"item":53,"name":13,"@type":44,"position":54},"https://docshare.wps.com/es/document/derivatives-derivative-table-and-exercises-with-solutions/68189/",4,{"url":53,"name":13,"@type":56,"author":57,"headline":13,"publisher":59,"fileFormat":62,"inLanguage":24,"description":14,"dateModified":63,"datePublished":64,"encodingFormat":62,"isAccessibleForFree":65,"interactionStatistic":66},"DigitalDocument",{"name":9,"@type":58},"Person",{"url":42,"name":60,"@type":61},"DocShare","Organization","application/pdf","2026-08-08","2026-07-14",true,{"@type":67,"interactionType":68,"userInteractionCount":20},"InteractionCounter",{"@type":69},"ViewAction",{"@type":71,"mainEntity":72},"FAQPage",[73,79,83],{"name":74,"@type":75,"acceptedAnswer":76},"¿Qué tipos de reglas de derivación se incluyen en la tabla?","Question",{"text":77,"@type":78},"Se incluyen reglas para constantes, potencias, sumas/diferencias, productos y funciones del tipo c·f(x) y f(x)·g(x), además de funciones compuestas.","Answer",{"name":80,"@type":75,"acceptedAnswer":81},"¿La guía incluye derivadas de funciones trigonométricas?",{"text":82,"@type":78},"Sí. Contiene derivadas relacionadas con sen, cos, tg, cotg y arcos (arc sen, arc cos, arc tg, arc cotg), aplicadas también a argumentos compuestos.",{"name":84,"@type":75,"acceptedAnswer":85},"¿Qué es la sección “Soluciones sin simplificar” y para qué sirve?",{"text":86,"@type":78},"Reúne el resultado derivado para los ejercicios manteniendo el desarrollo sin realizar simplificaciones, con el objetivo de practicar el procedimiento paso a paso.","https://schema.org",{"og:url":53,"og:type":89,"og:title":13,"og:site_name":60,"og:description":14},"article",{"robots":91,"canonical":53},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":94},[95,100,104,106,110,114,118,122,126,130],{"id":96,"doc_module":4,"doc_module_name":47,"category_name":97,"show_sort_weight":98,"slug":99},39,"Cómic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":47,"category_name":102,"show_sort_weight":98,"slug":103},43,"Estilo de Vida","lifestyle",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":98,"slug":105},"exam",{"id":107,"doc_module":4,"doc_module_name":47,"category_name":108,"show_sort_weight":98,"slug":109},44,"General","general",{"id":111,"doc_module":4,"doc_module_name":47,"category_name":112,"show_sort_weight":98,"slug":113},41,"Investigación e Informes","research-report",{"id":115,"doc_module":4,"doc_module_name":47,"category_name":116,"show_sort_weight":98,"slug":117},37,"Literatura","literature",{"id":119,"doc_module":4,"doc_module_name":47,"category_name":120,"show_sort_weight":98,"slug":121},22,"Relatos y Novelas","story-novel",{"id":123,"doc_module":4,"doc_module_name":47,"category_name":124,"show_sort_weight":98,"slug":125},42,"Religión y Espiritualidad","religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":47,"category_name":128,"show_sort_weight":98,"slug":129},40,"Salud y Atención Médica","healthcare",{"id":131,"doc_module":4,"doc_module_name":47,"category_name":132,"show_sort_weight":98,"slug":133},24,"Tecnología","technology"]