[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522822-105":59,"doc-detail-522822-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","infinite-calculus-chain-rule-with-trig-worksheet-3","Infinite Calculus - Chain Rule with Trig - Worksheet 3","","Worksheet on differentiating trigonometric functions using the chain rule, asking students to compute derivatives with respect to x for eight provided expressions. Problems include standard trig forms such as sine, tangent, secant, and cosecant, as well as composite functions where x appears in products and powers. Work is shown for select items, illustrating step-by-step application of the chain rule and derivative identities for trigonometric functions. Suitable for practice in differentiation with trig.",{"@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/infinite-calculus-chain-rule-with-trig-worksheet-3/522822/",{"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/infinite-calculus-chain-rule-with-trig-worksheet-3/522822.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":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the goal of this worksheet?","Question",{"text":112,"@type":113},"Differentiate each given function with respect to x using the chain rule and appropriate trigonometric derivatives.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What types of functions appear in the problems?",{"text":117,"@type":113},"The worksheet includes trigonometric functions like sin, tan, sec, and csc, plus composite expressions where the inside of the trig function involves powers and linear combinations of x.",{"name":119,"@type":110,"acceptedAnswer":120},"How is the chain rule applied in these problems?",{"text":121,"@type":113},"For composite trig functions, differentiate the outer trig function and multiply by the derivative of the inner expression, following the chain rule.","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},522822,1791489191,{"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":52,"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-Trigonometric Functions Date  Period   \nDifferentiate each function with respect to x.  \n1) f (x) = sin 2x3 2) y = tan 5x3  \n3) y = sec 4x5 4) y = csc 5x5  \n5) y = (2x5 + 3)cos x2  −2x2 − 5   \n6) y = 3 cos 2x  \n7) f (x) = sin 3 x 5 8) f (x) = cos (−3x2 + 2)2  \nKuta Software-Infinite Calculus Name   \nDifferentiation-Trigonometric Functions Date  Period   \nDifferentiate each function with respect to x.  \n1) f (x) = sin 2x3 2) y = tan 5x3  \nf ' (x) = cos 2x3 ⋅ 6x2  dy  \n2 3 = sec 2 5x3 ⋅ 15x2  \n= 6x cos 2x dx  \n= 15x2 ⋅ sec 2 5x3  \n3) y = sec 4x5 4) y = csc 5x5  \ndydx = sec 4x5 ⋅ tan 4x5 ⋅ 20x4 ~~ ~~dydx = −csc 5x5 ⋅ cot 5x5 ⋅ 25x4  \n= 20x4 sec 4x5 ⋅ tan 4x5 = −25x4 csc 5x5 ⋅ cot 5x5  \n5) y = (2x5 + 3)cos x2  −2x2 − 5   \n6) y = 3  \ncos 2x  \ndy = (2x5 + 3) ⋅ −1sin x 2 ⋅ 2x + cos x 2 ⋅ 10x4 3 2 3 2  \ndx  dy   cos 2x ⋅ −4x − (−2x − 5) ⋅ −1sin 2x ⋅ 6x   \n= 2x(−2x5 sin x2 − 3sin x2 + 5x3 cos x2 ) dx = cos 2 2x3  \n2x(−2cos 2x3 − 6x3 sin 2x3 − 15xsin 2x3 ) =  \ncos 2 2x3  \n7) f (x) = sin 3 x 5 8) f (x) = cos (−3x2 + 2)2  \nf ' (x) = 3 ⋅ sin 2 x 5 cos x 5 ⋅ 5x4 f ' (x) = −sin (−3x2 + 2)2 ⋅ 2(−3x2 + 2) ⋅ −6x = 15x4 ⋅ sin 2 x 5 cos x 5 = 12xsin (−3x2 + 2)2 ⋅ (−3x2 + 2)  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaiod3qpoV4woy","https://ap.wps.com/l/cbCaiod3qpoV4woy","pdf",27292,"English","# Differentiate each function with respect to x\n## Problem set 1-8","[{\"question\":\"What is the goal of this worksheet?\",\"answer\":\"Differentiate each given function with respect to x using the chain rule and appropriate trigonometric derivatives.\"},{\"question\":\"What types of functions appear in the problems?\",\"answer\":\"The worksheet includes trigonometric functions like sin, tan, sec, and csc, plus composite expressions where the inside of the trig function involves powers and linear combinations of x.\"},{\"question\":\"How is the chain rule applied in these problems?\",\"answer\":\"For composite trig functions, differentiate the outer trig function and multiply by the derivative of the inner expression, following the chain rule.\"}]","Infinite Calculus - Chain Rule with Trig - Worksheet 3 | PDF",1791426206]