[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523575-105":59,"doc-detail-523575-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-precalculus-definition-of-the-derivative","Infinite Precalculus - Definition of the Derivative","","Worksheets from Kuta Software-Infinite Precalculus focus on using the definition of the derivative to compute derivatives of given functions with respect to x. The problems provide multiple algebraic function forms and ask for derivatives in several numbered items. A critical thinking prompt then guides learners to inspect answers from problems 1–10, identify a pattern, and use it to predict the derivative of a related expression. Supporting explanations summarize rules applied to terms, constants, and exponents, connecting results to sum, constant, and power principles.",{"@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-precalculus-definition-of-the-derivative/523575/",{"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-precalculus-definition-of-the-derivative/523575.png","ImageObject",300,407,{"name":92,"@type":93},"dabgoudw","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":39},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does the worksheet ask you to do with the definition of the derivative?","Question",{"text":112,"@type":113},"Use the definition of the derivative to find the derivative of each given function with respect to x.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are the problems organized?",{"text":117,"@type":113},"There are numbered derivative problems (1–10) followed by a critical thinking question (11) that builds on your earlier answers.",{"name":119,"@type":110,"acceptedAnswer":120},"What key pattern or rules should you look for after solving problems 1–10?",{"text":121,"@type":113},"Identify how each term is handled independently, constants become 0, and exponents decrease by 1 while coefficients are multiplied by the original exponent.","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},523575,1791529482,{"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":39,"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},3985747860484,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Kuta Software-Infinite Precalculus 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 􀀠 􀀕x 􀀎 􀀕 2) y 􀀠 x 􀀎 􀀘  \n3) y 􀀠 􀀕x 􀀎 􀀘 4) y 􀀠 􀀘x 􀀎 􀀗  \n5) y 􀀠 􀀗x 􀀕 􀀎 􀀗 6) y 􀀠 􀀐􀀖 x 􀀕 􀀎 􀀕  \n7) y 􀀠 􀀐􀀗x 􀀕 􀀎 􀀔 8) y 􀀠 x 􀀕 􀀐 􀀘  \n9) f (x) 􀀠 x 􀀕 􀀎 x 􀀐 􀀔 10) f (x) 􀀠 􀀗x 􀀕 􀀎 􀀗x 􀀐 􀀖  \nCritical thinking question:  \n11) Look at your answers for problems 1-10. Try to determine a pattern to guess the derivative of y 􀀠 􀀕x 􀀕 􀀎 􀀖 x 􀀎 􀀚 .  \nKuta Software-Infinite Precalculus 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 􀀠 􀀕x 􀀎 􀀕 2) y 􀀠 x 􀀎 􀀘  \ndydx 􀀠 􀀕 ~~ ~~dydx 􀀠 􀀔  \n3) y 􀀠 􀀕x 􀀎 􀀘 4) y 􀀠 􀀘x 􀀎 􀀗  \ndydx 􀀠 􀀕 ~~ ~~dydx 􀀠 􀀘  \n5) y 􀀠 􀀗x 􀀕 􀀎 􀀗 6) y 􀀠 􀀐􀀖 x 􀀕 􀀎 􀀕  \ndydx 􀀠 􀀛 x ~~ ~~dydx 􀀠 􀀐􀀙x  \n7) y 􀀠 􀀐􀀗x 􀀕 􀀎 􀀔 8) y 􀀠 x 􀀕 􀀐 􀀘  \ndydx 􀀠 􀀐􀀛 x ~~ ~~dydx 􀀠 􀀕x  \n9) f (x) 􀀠 x 􀀕 􀀎 x 􀀐 􀀔 10) f (x) 􀀠 􀀗x 􀀕 􀀎 􀀗x 􀀐 􀀖  \nf ' (x) 􀀠 􀀕x 􀀎 􀀔 f ' (x) 􀀠 􀀛 x 􀀎 􀀗  \nCritical thinking question:  \n11) Look at your answers for problems 1-10. Try to determine a pattern to guess the derivative of y 􀀠 􀀕x 􀀕 􀀎 􀀖 x 􀀎 􀀚 .  \ndydx 􀀠 􀀗x 􀀎 􀀖 Each term is worked on independently and the new terms are added or subtracted as in the original function. Constants turn to 0s. Exponents for each term with x are decreased by 1. Coefficients are multiplied by the original exponent. This  \nillustrates the sum, constant, and power rules. You will learn them soon.  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaioGlniCRrAyl","https://ap.wps.com/l/cbCaioGlniCRrAyl","pdf",19928,"English","# Definition of the Derivative\n## Use the definition to find derivatives\n## Critical thinking pattern recognition","[{\"question\":\"What does the worksheet ask you to do with the definition of the derivative?\",\"answer\":\"Use the definition of the derivative to find the derivative of each given function with respect to x.\"},{\"question\":\"How are the problems organized?\",\"answer\":\"There are numbered derivative problems (1–10) followed by a critical thinking question (11) that builds on your earlier answers.\"},{\"question\":\"What key pattern or rules should you look for after solving problems 1–10?\",\"answer\":\"Identify how each term is handled independently, constants become 0, and exponents decrease by 1 while coefficients are multiplied by the original exponent.\"}]","Infinite Precalculus - Definition of the Derivative | PDF",1791427046]