[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522843-105":59,"doc-detail-522843-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","differentiation-quotient-rule-worksheets","Differentiation - Quotient Rule - Worksheets","","Infinite Calculus differentiation worksheet practice focuses on the quotient rule for finding derivatives with respect to x. It provides multiple problems asking students to differentiate given functions, including rational expressions and products inside quotient forms, with space for showing steps. A critical thinking task challenges a claim about the derivative of (fg)' and requires constructing an example using two functions f and g to disprove the statement.",{"@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/differentiation-quotient-rule-worksheets/522843/",{"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-quotient-rule-worksheets/522843.png","ImageObject",300,407,{"name":92,"@type":93},"Taylor Morgan","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-13","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What does this worksheet practice in differentiation?","Question",{"text":113,"@type":114},"It practices applying the quotient rule to differentiate functions with respect to x.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How many standard differentiation problems are included?",{"text":118,"@type":114},"There are 11 numbered problems asking students to differentiate each given function.",{"name":120,"@type":111,"acceptedAnswer":121},"What is required for the critical thinking problem (12)?",{"text":122,"@type":114},"It requires finding a counterexample to show that the derivative identity claimed by a classmate is wrong for any functions f and g.","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},522843,1791506896,{"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":19,"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":52},1099523885336,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Kuta Software-Infinite Calculus Name___________________________________  \nDifferentiation-Quotient Rule Date________________ Period____  \nDifferentiate each function with respect to x.  \n1) y = 2x42−~~ ~~5~~ ~~ 2) f (x) = ~~ ~~x~~ ~~5~~ ~~~~ ~~5~~ ~~  \n3) f (x) = 4x35+~~ ~~4~~ ~~ 4) y = 4x34x−3x42~~ ~~  \n3x4 + 2   4x5 + 2x2   \n5) y = 6) y =  \n3x3 − 2 3x4 + 5  \n4x5 + x2 + 4   3x4 + 5x3 − 5   \n7) y = 8) y =  \n5x2 − 2 2x4 − 4  \n9) y = x~~ ~~3~~ ~~−x5~~ ~~~~ ~~3~~ ~~  \n10) y = ~~ ~~x4~~ ~~+~~ ~~~~ ~~  \n3 − 4x  \n11) y = 4x4~~ ~~−~~ ~~45x2~~ ~~+~~ ~~5~~ ~~  \n3  \n2x + 3  \nCritical thinking question:  \n12) A classmate claims that (~~ ~~fg~~ ~~) ' = ~~ ~~fg~~ ~~''~~ ~~ for any functions f and g. Show an example that proves your  \nclassmate wrong.  \nKuta Software-Infinite Calculus  \nDifferentiation-Quotient Rule  \nDifferentiate each function with respect to x.  \n1) y = 2x42−~~ ~~5  \ndy 2 ⋅ 8x3  \n~~ ~~ = − ~~ ~~  \ndx (2x4 − 5) 2  \n 16x3 = −  \n4x8 − 20x4 + 25  \n3) f (x) = 4x35+~~ ~~4~~ ~~  \n 5 ⋅ 12x2  f ' (x) = −  \n(4x3 + 4)2  \n 15x2 = −  \n4x6 + 8x3 + 4  \n5) y = ~~ ~~3x3x43~~ ~~~~ ~~22  \ndy (3x3 − 2) ⋅ 12x3 − (3x4 + 2) ⋅ 9x2 ~~ ~~ = ~~  ~~dx (3x3 − 2)2  \n9x6 − 24x3 − 18x2 =  \n9x6 − 12x3 + 4  \n4x5 + x2 + 4   \n7) y =  \n5x2 − 2  \ndy   (5x2 − 2)(20x4 + 2x) − (4x5 + x2 + 4) ⋅ 10x =  \ndx (5x2 − 2)2  \n60x6 − 40x4 − 44x =  \n25x4 − 20x2 + 4  \n2) f  \n4) y  \n6) y  \n8) y  \nName___________________________________  \nDate________________ Period____  \n(x) = ~~ ~~x~~ ~~5~~ ~~~~ ~~5~~ ~~  \n 2 ⋅ 5x4  f ' (x) = −  \n( x5 − 5)2  \n 10x4   \n= −  \nx 10 − 10x5 + 25  \n=  \n4x3 − 3x2   \n4x5 − 4  \ndy (4x5 − 4)( 12x2 − 6x) − (4x3 − 3x2 ) ⋅ 20x4 ~~ ~~ = ~~  ~~dx (4x5 − 4)2  \n=  \n−8x7 + 9x6 − 12x2 + 6x  \n4x10 − 8x5 + 4  \n=  \n4x5 + 2x2  \n3x4 + 5  \ndy (3x4 + 5)(20x4 + 4x) − (4x5 + 2x2 ) ⋅ 12x3 ~~ ~~ = ~~  ~~dx (3x4 + 5)2  \n12x8 − 12x5 + 100x4 + 20x = ~~ ~~  \n9x8 + 30x4 + 25  \n=  \n3x4 + 5x3 − 5   \n2x4 − 4  \ndy (2x4 − 4)( 12x3 + 15x2 ) − (3x4 + 5x3 − 5) ⋅ 8x3 ~~ ~~ = ~~  ~~dx (2x4 − 4)2  \n−5x6 − 4x3 − 30x2 = ~~ ~~  \n2x8 − 8x4 + 8  \n9) y = x~~ ~~3~~ ~~−x5~~ ~~~~ ~~3~~ ~~  \ndy (x5 + 3)(3x2 − 2x) − (x3 − x2 − 3) ⋅ 5x4 ~~ ~~ = ~~  ~~dx (x5 + 3)2  \n=  \n−2x7 + 3x6 + 15x4 + 9x2 − 6x x 10 + 6x5 + 9  \n10) y = ~~ ~~x4~~ ~~+~~ ~~~~ ~~  \n3 − 4x  \ndy (3 − 4x−4 ) ⋅ 4x3 − (x4 + 6) ⋅ 16x−5  \n~~ ~~ = ~~ ~~  \ndx (3 − 4x−4 )2  \n 12x11 − 32x7 − 96x3   \n=  \n9x8 − 24x4 + 16  \n4x4 − 4x2 + 5   \n11) y =  \n5  \n3  \n2x + 3  \n(2x53 + 3)( 16x3 − 8x) − (4x4 − 4x2 + 5) ⋅  10  x~~ ~~23 dy 3  \n~~ ~~ = ~~  ~~dx   (2x~~ ~~53 + 3) 2    \n14 8 2  \n56x 3 + 144x3 − 8x 3 − 72x − 50x 3   \n=  \n 10   5  \n3 3  \n12x + 36x + 27  \nCritical thinking question:  \n12) A classmate claims that (~~ ~~fg~~ ~~) ' = ~~ ~~fg~~ ~~''~~ ~~ for any functions f and g. Show an example that proves your  \nclassmate wrong.  \nMany answers. Ex: f = 4, g = 2x, −  2  ≠ 0  \nx2  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaibPDbidwZIIh","https://ap.wps.com/l/cbCaibPDbidwZIIh","pdf",39832,"English","# Differentiation - Quotient Rule\n## Practice problems 1-11\n## Critical thinking problem 12","[{\"question\":\"What does this worksheet practice in differentiation?\",\"answer\":\"It practices applying the quotient rule to differentiate functions with respect to x.\"},{\"question\":\"How many standard differentiation problems are included?\",\"answer\":\"There are 11 numbered problems asking students to differentiate each given function.\"},{\"question\":\"What is required for the critical thinking problem (12)?\",\"answer\":\"It requires finding a counterexample to show that the derivative identity claimed by a classmate is wrong for any functions f and g.\"}]","Differentiation - Quotient Rule - Worksheets | PDF",1791426225]