[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-detail-522834-en":59,"doc-seo-522834-105":80},{"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":5,"data":60},{"doc_id":61,"user_id":62,"nickname":63,"user_avatar":64,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":66,"doc_content":67,"file_id":68,"file_url":69,"file_type":70,"file_size":71,"view_count":72,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":73,"language_code":74,"site_id":75,"html_lang":74,"table_of_contents":76,"faqs":77,"seo_title":78,"seo_description":66,"update_tm":79,"read_time":52,"preview_page_count":4},522834,1099523882367,"Jordan Avery","https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Implicit Differentiation - Worksheet 3","Worksheet practice on implicit differentiation. Problems 1–12 ask students to compute dy/dx in terms of x and y for a range of implicit equations involving polynomial expressions, products, and logarithms, as well as a trigonometric term. Problems 13–14 extend the skill by requiring the second derivative d²y/dx² in terms of x and y. A critical thinking question compares three different strategies—direct differentiation, clearing denominators, and solving for y—to verify whether results match and how to justify equivalence.","Kuta Software-Infinite Calculus Name___________________________________  \nImplicit Differentiation Date________________ Period____  \nFor each problem, use implicit differentiation to find dydx in terms of x and y.  \n1) 2x3 = 2 y2 + 5 2) 3x2 + 3 y2 = 2  \n3) 5 y2 = 2x3 − 5 y 4) 4x2 = 2 y3 + 4 y  \n5) 5x3 = −3xy + 2 6) 1 = 3x + 2x2y 2  \n7) 3x2y 2 = 4x2 − 4xy 8) 5x3 + xy 2 = 5x3y 3  \n9) 2x3 = (3xy + 1) 2 10) x 2 = (4x2y 3 + 1) 2  \n11) sin 2x2y 3 = 3x3 + 1 12) 3x2 + 3 = ln 5xy2  \nFor each problem, use implicit differentiation to find dd2222xy2222 in terms of x and y.  \n13) 4 y2 + 2 = 3x2 14) 5 = 4x2 + 5 y2  \nCritical thinking question:  \n15) Use three strategies to find dydx in terms of x and y, where ~~ ~~3x24~~ ~~y~~ ~~ = x. Strategy 1: Use implicit differentiation directly on the given equation. Strategy 2: Multiply both sides of the given equation by the denominator of the left side, then use implicit differentiation. Strategy 3: Solve for y, then differentiate. Do your three answers look the same? If not, how can you show that they are all correct answers?  \nKuta Software-Infinite Calculus Name___________________________________  \nImplicit Differentiation Date________________ Period____  \nFor each problem, use implicit differentiation to find dydx in terms of x and y.  \n1) 2x3 = 2 y2 + 5 2) 3x2 + 3 y2 = 2  \ndy   3x2   dy   x  \n= = −  \ndx 2 y dx y  \n3) 5 y2 = 2x3 − 5 y 4) 4x2 = 2 y3 + 4 y  \ndy   6x2   dy   4x   \n= =  \ndx 10 y + 5 dx 3 y2 + 2  \n5) 5x3 = −3xy + 2 6) 1 = 3x + 2x2y 2  \ndy   − y − 5x2   dy   −3 − 4xy2   \n= =  \ndx x dx 4x2y  \n7) 3x2y 2 = 4x2 − 4xy 8) 5x3 + xy 2 = 5x3y 3  \ndy   4x − 2 y − 3xy2   dy   15x2y 3 − 15x2 − y 2   \n= =  \ndx 3x2y + 2x dx 2xy − 15x3y 2  \n9) 2x3 = (3xy + 1) 2 10) x 2 = (4x2y 3 + 1) 2  \ndy   −3 y2x − y + x 2   dy   −32 y6x2 − 8 y3 + 1   \n= =  \ndx 3x2y + x dx 48x3y 5 + 12xy2  \n11) sin 2x2y 3 = 3x3 + 1  \ndy   9x − 4 y3 cos 2x2y 3 =  \ndx 6xy2 cos 2x2y 3  \n12) 3x2 + 3 = ln 5xy2  \ndy   6 yx2 − y  \n= dx 2x  \nFor each problem, use implicit differentiation to find dd2222xy2222 in terms of x and y.  \n13) 4 y2 + 2 = 3x2  \nd 2y   12 y2 − 9x2 =  \ndx2 16 y3  \n14) 5 = 4x2 + 5 y2  \nd 2y   −20 y2 − 16x2 =  \ndx2 25 y3  \nCritical thinking question:  \n15) Use three strategies to find dydx in terms of x and y, where ~~ ~~3x24~~ ~~y~~ ~~ = x. Strategy 1: Use implicit differentiation directly on the given equation. Strategy 2: Multiply both sides of the given equation by the denominator of the left side, then use implicit differentiation. Strategy 3: Solve for y, then differentiate. Do your three answers look the same? If not, how can you show that they are all correct answers?  \ndy   6xy − 4 y2   dy   6x − 4 y   dy   3  \nStrategy 1: dx = 3x2 , Strategy 2: dx = 4x , Strategy 3: dx = 4 To show all answers are the same, plug y = ~~ ~~3x4~~ ~~ into results for strategies 1 and 2.  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaig6FDPdWuSHm","https://ap.wps.com/l/cbCaig6FDPdWuSHm","pdf",38582,11,"English","en",105,"# Implicit Differentiation Practice\n## Find dy/dx in terms of x and y (1–12)\n## Find d²y/dx² in terms of x and y (13–14)\n## Critical thinking: compare three strategies (15)","[{\"question\":\"What do problems 1–12 ask for?\",\"answer\":\"Each problem asks you to use implicit differentiation to find dy/dx in terms of x and y for the given implicit equation.\"},{\"question\":\"How are problems 13–14 different from 1–12?\",\"answer\":\"They ask for the second derivative d²y/dx² in terms of x and y instead of dy/dx.\"},{\"question\":\"What are the three strategies in the critical thinking question?\",\"answer\":\"Strategy 1 differentiates the given equation implicitly directly. Strategy 2 multiplies both sides by the left-side denominator, then uses implicit differentiation. Strategy 3 solves for y and then differentiates.\"}]","Implicit Differentiation - Worksheet 3 | PDF",1791426217,{"code":4,"msg":81,"data":82},"ok",{"site_id":75,"language":74,"slug":83,"title":65,"keywords":84,"description":66,"schema_data":85,"social_meta":139,"head_meta":141,"extra_data":143,"updated_unix":144},"implicit-differentiation-worksheet-3","",{"@graph":86,"@context":138},[87,101,121],{"@type":88,"itemListElement":89},"BreadcrumbList",[90,94,96,99],{"item":91,"name":92,"@type":93,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":95,"name":9,"@type":93,"position":14},"https://docshare.wps.com/document/",{"item":97,"name":20,"@type":93,"position":98},"https://docshare.wps.com/document/exam/",3,{"item":100,"name":65,"@type":93,"position":19},"https://docshare.wps.com/document/implicit-differentiation-worksheet-3/522834/",{"url":100,"name":65,"@type":102,"image":103,"author":108,"headline":65,"publisher":110,"fileFormat":113,"inLanguage":74,"description":66,"dateModified":114,"datePublished":115,"encodingFormat":113,"isAccessibleForFree":116,"interactionStatistic":117},"DigitalDocument",{"url":104,"@type":105,"width":106,"height":107},"https://docshare.wps.com/thumbnails/implicit-differentiation-worksheet-3/522834.png","ImageObject",300,407,{"name":63,"@type":109},"Person",{"url":91,"name":111,"@type":112},"DocShare","Organization","application/pdf","2026-11-11","2026-10-08",true,{"@type":118,"interactionType":119,"userInteractionCount":72},"InteractionCounter",{"@type":120},"ViewAction",{"@type":122,"mainEntity":123},"FAQPage",[124,130,134],{"name":125,"@type":126,"acceptedAnswer":127},"What do problems 1–12 ask for?","Question",{"text":128,"@type":129},"Each problem asks you to use implicit differentiation to find dy/dx in terms of x and y for the given implicit equation.","Answer",{"name":131,"@type":126,"acceptedAnswer":132},"How are problems 13–14 different from 1–12?",{"text":133,"@type":129},"They ask for the second derivative d²y/dx² in terms of x and y instead of dy/dx.",{"name":135,"@type":126,"acceptedAnswer":136},"What are the three strategies in the critical thinking question?",{"text":137,"@type":129},"Strategy 1 differentiates the given equation implicitly directly. Strategy 2 multiplies both sides by the left-side denominator, then uses implicit differentiation. Strategy 3 solves for y and then differentiates.","https://schema.org",{"og:url":100,"og:type":140,"og:title":65,"og:site_name":111,"og:description":66},"article",{"robots":142,"canonical":100},"index,follow",{"doc_id":61,"site_id":75},1791519159]