[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522824-105":59,"doc-detail-522824-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","definition-of-the-derivative-part-3-calculus-practice-worksheet","Definition of the Derivative - Part 3 - Calculus Practice Worksheet","","This document provides a set of calculus practice problems focused on applying the formal definition of the derivative to various functions, including linear, quadratic, and rational functions. It includes a total of 10 problems that require students to compute derivatives with respect to x, as well as one critical thinking question that asks students to demonstrate why the derivative of a function does not exist at a specific point. The document serves as an effective review tool for students learning fundamental calculus concepts and differentiation techniques through direct calculation.",{"@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/definition-of-the-derivative-part-3-calculus-practice-worksheet/522824/",{"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/definition-of-the-derivative-part-3-calculus-practice-worksheet/522824.png","ImageObject",300,407,{"name":92,"@type":93},"Riley West","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-19","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does this worksheet focus on?","Question",{"text":112,"@type":113},"The worksheet focuses on using the limit-based definition of the derivative to find the derivative of various linear, quadratic, and rational functions.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How many problems are included in the exercise?",{"text":117,"@type":113},"There are 10 practice problems provided, followed by one critical thinking question related to the existence of a derivative at a specific point.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the objective of the critical thinking question?",{"text":121,"@type":113},"The question asks students to use the definition of the derivative to prove that the derivative of the function f(x) = sqrt(x) does not exist at x = 0 by analyzing the left-handed and right-handed limits.","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},522824,1791534308,{"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":34,"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___________________________________  \nDefinition of the Derivative Date________________ Period____  \nUse the definition of the derivative to find the derivative of each function with respect to x.  \n1) y = −2x + 5 2) f (x) = −4x − 2  \n3) y = 4x2 + 1 4) f (x) = −3x2 + 4  \n5) y = −4x2 − 5x − 2 6) y = 3x2 + 3x + 3  \n7) y =  −3x − 5 8) f (x) = 4x − 5   \n1 2  \n9) y = 10) f (x) = −  \nx + 2 2x − 1  \nCritical thinking question:  \n11) Use the definition of the derivative to show that f ' (0) does not exist where f (x) =  x  .  \nKuta Software-Infinite Calculus Name   \nDefinition of the Derivative Date  Period   \nUse the definition of the derivative to find the derivative of each function with respect to x.  \n1) y = −2x + 5  \ndy  \n~~ ~~ = −2 dx  \n3) y = 4x2 + 1  \ndydx = 8x  \n5) y = −4x2 − 5x − 2  \ndydx = −8x − 5  \n7) y = −3x − 5  \ndy   3 = −  \ndx 2 −3x − 5  \n9) y = x~~ ~~~~ ~~2  \ndy   1 = −  \ndx x 2 + 4x + 4  \n2) f (x) = −4x − 2  \nf ' (x) = −4  \n4) f (x) = −3x2 + 4  \nf ' (x) = −6x  \n6) y = 3x2 + 3x + 3  \ndydx = 6x + 3  \n8) f (x) = 4x − 5  \nf ' (x) =  2   \n4x − 5  \n10) f (x) = − ~~ ~~2x~~ ~~1  \nf ' (x) = ~~ ~~4x2~~ ~~−~~ ~~44x~~ ~~+~~ ~~1~~ ~~  \nCritical thinking question:  \n11) Use the definition of the derivative to show that f ' (0) does not exist where f (x) =  x  .  \n  0 + h  −  0     h    \nUsing 0 in the definition, we have lim = lim which does not exist because  \nh→ 0 h h→ 0 h  \nthe left-handed and right-handed limits are different.  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaigaC95bTEgFp","https://ap.wps.com/l/cbCaigaC95bTEgFp","pdf",27910,"English","# Calculus Practice Exercises\n## Definition of the Derivative Problems\n## Critical Thinking Challenge","[{\"question\":\"What does this worksheet focus on?\",\"answer\":\"The worksheet focuses on using the limit-based definition of the derivative to find the derivative of various linear, quadratic, and rational functions.\"},{\"question\":\"How many problems are included in the exercise?\",\"answer\":\"There are 10 practice problems provided, followed by one critical thinking question related to the existence of a derivative at a specific point.\"},{\"question\":\"What is the objective of the critical thinking question?\",\"answer\":\"The question asks students to use the definition of the derivative to prove that the derivative of the function f(x) = sqrt(x) does not exist at x = 0 by analyzing the left-handed and right-handed limits.\"}]","Definition of the Derivative - Part 3 - Calculus Practice Worksheet | PDF",1791426209]