[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522837-105":59,"doc-detail-522837-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","differentiation-power-constant-and-sum-rules-worksheet-03","Differentiation - Power, Constant, and Sum Rules - Worksheet 03","","Worksheets for Infinite Calculus practice focusing on differentiation using power, constant, and sum rules. Problems ask learners to differentiate various algebraic functions with respect to x or another given variable such as r, s, and h. The set includes expressions with powers, constants, negative exponents, and multiple terms, requiring computation of derivatives and simplified results. Answers are guided step-by-step through derivative notation and arithmetic simplification rules.",{"@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/differentiation-power-constant-and-sum-rules-worksheet-03/522837/",{"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-power-constant-and-sum-rules-worksheet-03/522837.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":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What differentiation rules are practiced in this worksheet?","Question",{"text":112,"@type":113},"It focuses on the power rule, constant rule, and sum rule for taking derivatives of algebraic functions.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which variables do the problems differentiate with respect to?",{"text":117,"@type":113},"Most tasks differentiate with respect to x, and some ask for differentiation with respect to other given variables like r and s.",{"name":119,"@type":110,"acceptedAnswer":120},"How do multi-term expressions get differentiated?",{"text":121,"@type":113},"Each term is differentiated separately using the relevant rule, then combined according to the sum rule to form the final derivative.","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},522837,1791519177,{"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":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"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":52},1099523885336,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Kuta Software-Infinite Calculus Name   \nDifferentiation-Power, Constant, and Sum Rules Date  Period   \nDifferentiate each function with respect to x.  \n1) y = 5 2) f (x) = 5x18  \n3) y = 4x5 + x 4) f (x) = 4x4 − 5x − 3  \n54~~ ~~ 5 23  \n5) y = 3x 6) y = 4  x  \n7) y = −4x−5 8) y = 3x3~~ ~~  \n23~~ ~~ 10) f ( x) = −2 x  \n9) y = x  \n2  5  \n11) y = ~~ ~~3~~ ~~ x 4 + 5x − x−3 12) y = − ~~ ~~12x4 + 3x 3 + 2x  \nDifferentiate each function with respect to the given variable.  \n13) y = −3r5 − 5r2 3 4  \n14) f (s) = −  s 2 −  s 4  \n3   3  16) h(s) = 2 ⋅ s + 2 ⋅ s  \n15) f (x) = ~~ ~~23x 2 − 34x 5  \nDifferentiate each function with respect to x. Problems may contain constants a, b, and c.  \n17) y = 5c 18) y = 4ax3a − bx3c  \nKuta Software-Infinite Calculus Name   \nDifferentiation-Power, Constant, and Sum Rules Date  Period   \nDifferentiate each function with respect to x.  \n1) y = 5  \ndy  \n~~ ~~ = 0  \ndx  \n3) y = 4x5 + x  \ndydx = 20x4 + 1  \n5  \n4  \n5) y = 3x  \n 1   \n4  \ndy 15x  \n~~ ~~ = ~~ ~~  \ndx 4  \n7) y = −4x−5  \ndy −6  \ndx = 20x  \n20  \n= ~~ ~~  \nx 6  \n2  \n3  \n9) y = x  \n1  \ndy 2 −  3  \n~~ ~~ = ~~ ~~ x  \ndx 3  \n2  \n= ~~ ~~  \n1  \n3  \n3x  \n2) f (x) = 5x18  \nf ' (x) = 90x17  \n4) f (x) = 4x4 − 5x − 3  \nf ' (x) = 16x3 − 5  \n5 23  \n6) y = 4  x  \ndy 5 − ~~ ~~13 ~~ ~~ = ~~ ~~ x  \ndx 6 5  \n= ~~ ~~  \n 1   \n3 6x  \n8) y =  3  x 3  \ndydx = −9x−4 9  \n= − ~~  ~~x 4  \n10) f ( x) = −2 x  \n3 f ' (x) = − ~~ ~~12x −  4  \n1  \n= − ~~ ~~  \n3  \n4 2x  \n2 4 −3  \n11) y =  3  x + 5x − x  \ndydx = ~~ ~~83x 3 + 5 + 3x−4  \n8x3 3 = ~~ ~~ + 5 + ~~ ~~  \n3 x4  \n5  \n12) y = − ~~ ~~12x4 + 3x 3 + 2x  \n2 dydx = −2x3 + 5x 3  + 2  \nDifferentiate each function with respect to the given variable.  \n13) y = −3r5 − 5r2 3 4  \n14) f (s) = −  s 2 −  s 4  \ndy 4  \n~~ ~~ = −15r − 10r  \ndr f ' (s) = 6s−3 + 16s−5  \n= ~~ ~~63 + ~~ ~~165  \ns s  \n2 32~~ ~~ 3 35~~ ~~ 16) h(s) =  ⋅ s +  ⋅ s  \n15) f (x) = ~~ ~~ x − ~~ ~~ x  \n3 4  2   4  \n1 − 1 −  \n1   2  h ' (s) =  3  s 3  +  5  s 5   \n2 9 − 5  \nf ' (x) = x − ~~ ~~ x 2 2  \n20 = ~~ ~~ + ~~ ~~  \n1  2   4  \n2  9 3 5 = x − ~~  ~~2~~  ~~ 3s 5s  \n5  \n20x  \nDifferentiate each function with respect to x. Problems may contain constants a, b, and c.  \n17) y = 5c  \ndy ~~ ~~ = 0 dx  \n18) y = 4ax3a − bx3c  \ndydx = 12a2 x 3a − 1 − 3bcx3c − 1  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaiaT9qugKi52Q","https://ap.wps.com/l/cbCaiaT9qugKi52Q","pdf",39523,"English","# Differentiate with respect to x\n## Problems using power, constant, and sum rules\n# Differentiate with respect to a given variable\n## Practice with r and s","[{\"question\":\"What differentiation rules are practiced in this worksheet?\",\"answer\":\"It focuses on the power rule, constant rule, and sum rule for taking derivatives of algebraic functions.\"},{\"question\":\"Which variables do the problems differentiate with respect to?\",\"answer\":\"Most tasks differentiate with respect to x, and some ask for differentiation with respect to other given variables like r and s.\"},{\"question\":\"How do multi-term expressions get differentiated?\",\"answer\":\"Each term is differentiated separately using the relevant rule, then combined according to the sum rule to form the final derivative.\"}]","Differentiation - Power, Constant, and Sum Rules - Worksheet 03 | PDF",1791426222]