[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522826-105":59,"doc-detail-522826-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","derivatives-of-inverse-functions-part-3-calculus-practice-worksheet","Derivatives of Inverse Functions - Part 3 - Calculus Practice Worksheet","","This calculus practice worksheet from Kuta Software focuses on the calculation of derivatives for inverse functions. The document provides structured exercises requiring students to find the derivative of an inverse function, denoted as (f^-1)'(x), using three distinct methods: direct computation, the derivative theorem (f^-1)'(x) = 1/f'(f^-1(x)), and the reciprocal formula dy/dx = 1/(dx/dy). The exercises cover linear and polynomial functions, guiding students through applying these essential calculus techniques.",{"@graph":69,"@context":123},[70,84,106],{"@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/derivatives-of-inverse-functions-part-3-calculus-practice-worksheet/522826/",{"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/derivatives-of-inverse-functions-part-3-calculus-practice-worksheet/522826.png","ImageObject",300,407,{"name":92,"@type":93},"Jordan Avery","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",11,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"How is the derivative of an inverse function calculated using the theorem?","Question",{"text":113,"@type":114},"The theorem states that (f^-1)'(x) = 1 / f'(f^-1(x)). This requires finding the derivative of the original function and evaluating it at the inverse function's value.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What is the alternative formula for finding the derivative of an inverse function mentioned in the document?",{"text":118,"@type":114},"The document also suggests using the formula dy/dx = 1 / (dx/dy), where y = f^-1(x), to find the derivative of the inverse function.",{"name":120,"@type":111,"acceptedAnswer":121},"What types of functions are provided as examples in this worksheet?",{"text":122,"@type":114},"The examples include linear functions such as f(x) = -3x + 3, as well as polynomial functions including cubic and higher-order polynomials like f(x) = -4x^3 - 4 and f(x) = x^7 + x - 3.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},522826,1791518987,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":24,"preview_page_count":4},1099523882367,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Kuta Software-Infinite Calculus Name___________________________________  \nDerivatives of Inverse Functions Date________________ Period____  \nFor each problem, find ( f −− 1) ' (x) by direct computation.  \n1) f (x) = −3x + 3 2) f (x) = −2x + 3  \nFor each problem, find ( f −− 1) ' (x) by using the theorem ( f −− 1) ' (x) = ~~ ~~f~~ ~~'~~ ~~(~~ ~~f1(x))  \n3) f (x) = −5x + 1 4) f (x) = −2x + 2  \n5) f ( x) = −2x − 3 6) f (x) = −4x3 − 4  \nFor each problem, find ( f −− 1) ' (x) by using the formula dydx = ~~  ~~1111dx~~ ~~, where y = f −− 1(x)  \ndy  \n7) f (x) = x 7 + x − 3 8) f (x) = 3x5 + 2x + 5  \nKuta Software-Infinite Calculus Name   \nDerivatives of Inverse Functions Date  Period   \nFor each problem, find ( f −− 1) ' (x) by direct computation.  \n1) f (x) = −3x + 3  \n( f −1 ) ' (x) = − ~~ ~~13  \n2) f (x) = −2x + 3  \n( f −1 ) ' (x) = − ~~ ~~12  \nFor each problem, find ( f −− 1) ' (x) by using the theorem ( f −− 1) ' (x) = ~~ ~~f~~ ~~'~~ ~~(~~ ~~f1(x))  \n3) f (x) = −5x + 1 4) f (x) = −2x + 2  \n( f −1 ) ' (x) = − ~~ ~~15~~ ~~ ( f −1 ) ' (x) = − ~~ ~~12  \n5) f ( x) = −2x − 3  \n( f −1 ) ' (x) = − ~~ ~~2x2  \n6) f (x) = −4x3 − 4  \n( f −1 ) ' (x) = − ~~ ~~1~~  ~~2  \n12 ⋅ (−x~~ ~~4~~ ~~ ) 3  \nFor each problem, find ( f −− 1) ' (x) by using the formula dydx = ~~  ~~1111dx~~ ~~, where y = f −− 1(x)  \ndy  \n7) f (x) = x 7 + x − 3  \n( f −1 ) ' (x) = ~~ ~~7~~ ~~y61+~~ ~~1  \n8) f (x) = 3x5 + 2x + 5  \n( f −1 ) ' (x) = ~~ ~~15~~ ~~y14~~ ~~+~~ ~~2  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaiihpD3gqkdBn","https://ap.wps.com/l/cbCaiihpD3gqkdBn","pdf",28740,"English","# Direct Computation\n## Inverse Function Derivatives\n# Derivative Theorem Applications\n## Using the Inverse Theorem\n# Reciprocal Derivative Formulas\n## Applying dy/dx = 1/(dx/dy)","[{\"question\":\"How is the derivative of an inverse function calculated using the theorem?\",\"answer\":\"The theorem states that (f^-1)'(x) = 1 / f'(f^-1(x)). This requires finding the derivative of the original function and evaluating it at the inverse function's value.\"},{\"question\":\"What is the alternative formula for finding the derivative of an inverse function mentioned in the document?\",\"answer\":\"The document also suggests using the formula dy/dx = 1 / (dx/dy), where y = f^-1(x), to find the derivative of the inverse function.\"},{\"question\":\"What types of functions are provided as examples in this worksheet?\",\"answer\":\"The examples include linear functions such as f(x) = -3x + 3, as well as polynomial functions including cubic and higher-order polynomials like f(x) = -4x^3 - 4 and f(x) = x^7 + x - 3.\"}]","Derivatives of Inverse Functions - Part 3 - Calculus Practice Worksheet | PDF",1791426211]