[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522831-105":59,"doc-detail-522831-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","higher-order-derivatives-chapter-3-calculus-practice-worksheet","Higher Order Derivatives - Chapter 3 - Calculus Practice Worksheet","","This calculus worksheet provides a structured set of practice problems focused on calculating higher-order derivatives of various functions. Designed as an educational resource for students, it includes exercises ranging from basic polynomial differentiation to more complex applications involving negative exponents and critical thinking questions. Each problem requires the student to compute specific derivatives, such as second, third, or fourth-order derivatives with respect to x. The document includes a comprehensive answer key at the end, making it an ideal tool for self-assessment and mastery of calculus differentiation techniques. The inclusion of conceptual challenges, such as the n-th derivative of a power function, encourages a deeper understanding of mathematical patterns and the use of factorial notation in calculus.",{"@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/higher-order-derivatives-chapter-3-calculus-practice-worksheet/522831/",{"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/higher-order-derivatives-chapter-3-calculus-practice-worksheet/522831.png","ImageObject",300,407,{"name":92,"@type":93},"Jordan Avery","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",13,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is the second derivative of the function y = -x^2?","Question",{"text":113,"@type":114},"The second derivative is -2.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How is the third derivative of y = -4x determined?",{"text":118,"@type":114},"The first derivative is -4, the second is 0, and therefore the third derivative is 0.",{"name":120,"@type":111,"acceptedAnswer":121},"What is the 100th derivative of y = 99x^99?",{"text":122,"@type":114},"The 99th derivative is a constant, so the 100th derivative is 0.","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},522831,1791518795,{"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":14,"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":24,"preview_page_count":4},1099523882367,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Kuta Software-Infinite Calculus Name   \nHigher Order Derivatives Date  Period   \nFor each problem, find the indicated derivative with respect to x.  \nd 2y 2) f (x) = 4x3 Find f ''  \n1) y = −x2 Find  dx2  \nd 3y 4) f (x) = 5x4 Find f '''  \n3) y = −4x Find ~~ ~~  \ndx 3  \nd 4y   d 3y  \n5) y = −5x4 Find 4 6) y = 3x5 − 2x Find 3 dx dx  \n7) y = −2x3 − 4x−3 Find ~~ ~~d3dxy3~~ ~~ 8) y = −x2 + 2 x Find ~~ ~~d3dxy3  \nCritical thinking questions. Find the indicated derivatives with respect to x.  \n9) y = 99x99 Find ~~ ~~d1dx0100y0~~ ~~ 10) f (x) = x 99 Find f (99)  \nKuta Software-Infinite Calculus Name   \nHigher Order Derivatives Date  Period   \nFor each problem, find the indicated derivative with respect to x.  \n2 d 2y  \n1) y = −x Find  dx2  \nd 2y  \n~~ ~~ = −2  \ndx2  \nd 3y  \n3) y = −4x Find dx 3  \nd 3y  \n= 0  \ndx 3  \n4  d 4y  \n5) y = −5x Find dx4  \nd 4y  \n= −120 dx4  \n3 −3  d 3y 7) y = −2x − 4x Find 3  \ndx  \nd 3y 240  \n~~ ~~ = −12 + ~~  ~~dx 3 x 6  \n2) f (x) = 4x3 Find f ''  \nf '' (x) = 24x  \n4) f (x) = 5x4 Find f '''  \nf ''' (x) = 120x  \n5 d 3y 6) y = 3x − 2x Find  dx 3  \nd3dxy3 = 180x2  \n2 5 2 d 3y 8) y = −x + 2 x Find  dx 3  \nd 3y 96  \n~~ ~~ = ~~  ~~dx 3 ~~ ~~135  \n125x  \nCritical thinking questions. Find the indicated derivatives with respect to x.  \n99  d 100y  10) f (x)  \n9) y = 99x Find 100  \ndx 99!  \nThe 99th derivative is a constant, so 100th derivative is 0.  \n= x 99 Find f (Made easy by  \n(99)  \nfactorial notation)  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaiqVJ2r7X4nIV","https://ap.wps.com/l/cbCaiqVJ2r7X4nIV","pdf",28236,"English","# Higher Order Derivatives Practice\n## Differentiation Problems\n## Critical Thinking Questions\n## Answer Key","[{\"question\":\"What is the second derivative of the function y = -x^2?\",\"answer\":\"The second derivative is -2.\"},{\"question\":\"How is the third derivative of y = -4x determined?\",\"answer\":\"The first derivative is -4, the second is 0, and therefore the third derivative is 0.\"},{\"question\":\"What is the 100th derivative of y = 99x^99?\",\"answer\":\"The 99th derivative is a constant, so the 100th derivative is 0.\"}]","Higher Order Derivatives - Chapter 3 - Calculus Practice Worksheet | PDF",1791426214]