[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522818-105":59,"doc-detail-522818-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","differentiation-inverse-trigonometric-functions-practice-worksheet","Differentiation-Inverse Trigonometric Functions - Practice Worksheet","","This document provides a comprehensive set of practice problems for calculating the derivatives of inverse trigonometric functions. It includes a series of differentiation exercises involving complex arguments and exponents, followed by detailed step-by-step solutions for each problem. Designed for students and educators in calculus courses, the material demonstrates the application of the chain rule in conjunction with standard inverse trigonometric differentiation formulas. It serves as an essential resource for mastering advanced derivative techniques in a classroom or self-study environment, emphasizing procedural accuracy and algebraic simplification.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/differentiation-inverse-trigonometric-functions-practice-worksheet/522818/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/differentiation-inverse-trigonometric-functions-practice-worksheet/522818.png","ImageObject",300,407,{"name":92,"@type":93},"Riley West","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What are the primary functions covered in these differentiation exercises?","Question",{"text":112,"@type":113},"The exercises focus on the derivatives of inverse trigonometric functions, including arcsine, arccosine, arctangent, and arccosecant, often involving composite arguments and powers.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are the solutions structured in the document?",{"text":117,"@type":113},"Each problem is presented with its original function, and the provided solutions show the application of the chain rule to derive the result, followed by necessary algebraic simplification.",{"name":119,"@type":110,"acceptedAnswer":120},"What mathematical techniques are required to solve these problems?",{"text":121,"@type":113},"To solve these problems, one must be familiar with the derivative formulas for inverse trigonometric functions and the chain rule for differentiating composite functions.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},522818,1791732628,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":29,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":24,"preview_page_count":4},1099523885074,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Kuta Software-Infinite Calculus Name   \nDifferentiation-Inverse Trigonometric Functions Date  Period   \nDifferentiate each function with respect to x.  \n1) y = cos−1 −5x3 2) y = sin −1 −2x2  \n3) y = tan −1 2x4 4) y = csc −1 4x2  \n5) y = (sin−1 5x2 ) 3 6) y = sin−1 (3x5 + 1) 3  \n7) y = (cos−1 4x2 ) 2 8) y = cos−1 (−2x3 − 3) 3  \nKuta Software-Infinite Calculus Name   \nDifferentiation-Inverse Trigonometric Functions Date  Period   \nDifferentiate each function with respect to x.  \n1) y = cos−1 −5x3  \ndy   1  2  \n= − ⋅ −15x dx 1 − (−5x3 )2   \n 15x2 =  \n1 − 25x6  \n3) y = tan −1 2x4  \ndy =  1  ⋅ 8x3  \ndx (2x4 )2 + 1  \n 8x3   \n=  \n4x8 + 1  \n5) y = (sin−1 5x2 ) 3  \ndydx = 3 ⋅ (sin−1 5x2 )2 ⋅ ~~ ~~1(5x2~~ ~~)2~~ ~~ ⋅ 10x  \n30x ⋅ (sin−1 5x2 )2 =  \n1 − 25x4  \n7) y = (cos−1 4x2 ) 2  \ndy = 2cos−1 4x2 ⋅ −  1  ⋅ 8x dx 1 − (4x2 )2   \n 16xcos−1 4x2 = −  \n1 − 16x4  \n2) y = sin −1 −2x2  \ndy   1   \n= ⋅ −4x dx 1 − (−2x2 )2   \n 4x   \n= −  \n1 − 4x4  \n4) y = csc −1 4x2  \ndy   1   \n= − ⋅ 8x dx  4x2  (4x2 )2 − 1   \n2  \n= − ~~ ~~  \nx 16x4 − 1  \n6) y = sin−1 (3x5 + 1) 3  \ndy =  1  ⋅ 3(3x5 + 1)2 ⋅ 15x4 dx 1 − ((3x5 + 1) 3 )2   \n 45x4 (3x5 + 1) 2 =  \n 1 − (3x5 + 1) 6   \n8) y = cos−1 (−2x3 − 3) 3  \ndy = −  1  ⋅ 3(−2x3 − 3)2 ⋅ −6x2 dx 1 − ((−2x3 − 3) 3 ) 2   \n 18x2 (−2x3 − 3) 2 =  \n 1 − (−2x3 − 3) 6   \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaitZdTulobxNt","https://ap.wps.com/l/cbCaitZdTulobxNt","pdf",28167,"English","# Practice Problems\n## Detailed Solutions","[{\"question\":\"What are the primary functions covered in these differentiation exercises?\",\"answer\":\"The exercises focus on the derivatives of inverse trigonometric functions, including arcsine, arccosine, arctangent, and arccosecant, often involving composite arguments and powers.\"},{\"question\":\"How are the solutions structured in the document?\",\"answer\":\"Each problem is presented with its original function, and the provided solutions show the application of the chain rule to derive the result, followed by necessary algebraic simplification.\"},{\"question\":\"What mathematical techniques are required to solve these problems?\",\"answer\":\"To solve these problems, one must be familiar with the derivative formulas for inverse trigonometric functions and the chain rule for differentiating composite functions.\"}]","Differentiation-Inverse Trigonometric Functions - Practice Worksheet | PDF",1791426203]