[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-522830-105":59,"doc-detail-522830-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-rules-with-tables-part-3-worksheet","Differentiation Rules with Tables - Part 3 - Worksheet","","Worksheets using Infinite Calculus-style differentiation rules with tables of values for two differentiable functions f(x), g(x) and their derivatives. Each problem provides a table and asks for derivatives of combinations h(x)=f(x)+g(x), h(x)=f(x)-g(x), h(x)=f(x)·g(x), products/quotients and compositions using the given derivative data. Answers are determined by applying standard derivative rules to the tabulated values at specified x points.",{"@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-rules-with-tables-part-3-worksheet/522830/",{"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-rules-with-tables-part-3-worksheet/522830.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":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What information is provided for each differentiation problem?","Question",{"text":112,"@type":113},"Each problem provides a table of values for f(x), f'(x), g(x), and g'(x) at specific x values.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do you find h'(x) when h(x)=f(x)+g(x)?",{"text":117,"@type":113},"Use the sum rule: h'(x)=f'(x)+g'(x), then substitute the tabulated derivatives at the requested x value.",{"name":119,"@type":110,"acceptedAnswer":120},"What rule applies when h(x)=f(x)·g(x) and you need h'(x)?",{"text":121,"@type":113},"Use the product rule: h'(x)=f(x)g'(x)+g(x)f'(x), then use the table values at the specified x point.","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},522830,1791666717,{"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":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,"preview_page_count":4},1099523882367,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Kuta Software-Infinite Calculus Name   \nDifferentiation Rules, with Tables Date  Period   \nFor each problem, you are given a table containing some values of differentiable functions f (x), g(x) and their derivatives. Use the table data and the rules of differentiation to solve each problem.  \n1)  \n\n| x | f ( x) | f ' ( x) | g( x) | g ' ( x) |\n| --- | --- | --- | --- | --- |\n| 1 | 2 | 1 | 1 | 2 |\n| 2 | 3 | 0 | 3 | 0 |\n| 3 | 2 | −1 | 1 | −2 |\n\nGiven h( x) = f ( x) + g( x), find h ' ( 1)  \n2)  \n\n| x | f (x) | f ' (x) | g(x) | g ' (x) |\n| --- | --- | --- | --- | --- |\n| 1 | 2 | −1 | 1 | 1 |\n| 2 | 1 |  1\u003Cbr>2 | 2 | 1 |\n| 3 | 3 | 2 | 3 | 1 |\n\nGiven h(x) = f (x) − g(x), find h ' (2)  \n3)  \n\n| x | f (x) | f ' (x) | g(x) | g ' (x) |\n| --- | --- | --- | --- | --- |\n| 1 | 2 | −1 | 1 | 2 |\n| 2 | 1 |  1\u003Cbr>2 | 3 | 0 |\n| 3 | 3 | 2 | 1 | −2 |\n\nGiven h(x) = f (x) ⋅ g(x), find h ' (3)  \n4)  \n\n| x | f (x) | f ' (x) | g(x) | g ' (x) |\n| --- | --- | --- | --- | --- |\n| 1 | 3 | −1 | 2 | −1 |\n| 2 | 2 | −1 | 1 | 0 |\n| 3 | 1 | −1 | 2 | 1 |\n\nGiven h(x) = ~~ ~~fg((xx))~~ ~~ , find h ' (3)  \n5)  \n\n| x | f (x) | f ' (x) | g(x) | g ' (x) |\n| --- | --- | --- | --- | --- |\n| 1 | 5 | −1 | 1 | 2 |\n| 2 | 4 | −1 | 3 | 3\u003Cbr>2 |\n| 3 | 3 | −1 | 4 | 1 |\n| 4 | 2 | −1 | 5 | 1 |\n| 5 | 1 | 0 | 6 |  1\u003Cbr>−\u003Cbr>2 |\n| 6 | 2 | 1 | 4 | −2 |\n\nPart 1) Given h1 (x) = f (x) + g(x), find h1 ' (2)  \nPart 2) Given h2 (x) = f (x) − g(x), find h2 ' (3)  \nPart 3) Given h3 (x) = f (x) ⋅ g(x), find h3 ' (4)  \nf (x)   \nPart 4) Given h4 (x) = , find h4 ' (2)  \ng( x)  \nPart 5) Given h5 ( x) = ( f ( x))2 , find h5 ' (2)  \nPart 6) Given h6 ( x) = f ( g( x)), find h6 ' (6)  \nKuta Software-Infinite Calculus Name   \nDifferentiation Rules, with Tables Date  Period   \nFor each problem, you are given a table containing some values of differentiable functions f (x), g(x) and their derivatives. Use the table data and the rules of differentiation to solve each problem.  \n1)  \n2)  \n\n| x | f ( x) | f ' ( x) | g( x) | g ' ( x) |\n| --- | --- | --- | --- | --- |\n| 1 | 2 | 1 | 1 | 2 |\n| 2 | 3 | 0 | 3 | 0 |\n| 3 | 2 | −1 | 1 | −2 |\n\nh ' ( 1) = f ' ( 1) + g ' ( 1) = 3  \n\n| x | f (x) | f ' (x) | g(x) | g ' (x) |\n| --- | --- | --- | --- | --- |\n| 1 | 2 | −1 | 1 | 1 |\n| 2 | 1 |  1\u003Cbr>2 | 2 | 1 |\n| 3 | 3 | 2 | 3 | 1 |\n\nh ' (2) = f ' (2) − g ' (2) = − ~~ ~~12  \nGiven h( x) = f ( x) + g( x), find h ' ( 1)  \nGiven h(x) = f (x) − g(x), find h ' (2)  \n3)  \n\n| x | f (x) | f ' (x) | g(x) | g ' (x) |\n| --- | --- | --- | --- | --- |\n| 1 | 2 | −1 | 1 | 2 |\n| 2 | 1 |  1\u003Cbr>2 | 3 | 0 |\n| 3 | 3 | 2 | 1 | −2 |\n\nGiven h(x) = f (x) ⋅ g(x), find h ' (3)  \nh ' (3) = f (3) ⋅ g ' (3) + g(3) ⋅ f ' (3) = −4  \n4)  \n\n| x | f (x) | f ' (x) | g(x) | g ' (x) |\n| --- | --- | --- | --- | --- |\n| 1 | 3 | −1 | 2 | −1 |\n| 2 | 2 | −1 | 1 | 0 |\n| 3 | 1 | −1 | 2 | 1 |\n\nGiven h(x) = ~~ ~~fg((xx))~~ ~~ , find h ' (3)  \ng(3) ⋅ f ' (3) − f (3) ⋅ g ' (3) 3  \nh ' (3) = ~~ ~~ = − ~~ ~~  \n(g(3))2 4  \n5)  \n\n| x | f (x) | f ' (x) | g(x) | g ' (x) |\n| --- | --- | --- | --- | --- |\n| 1 | 5 | −1 | 1 | 2 |\n| 2 | 4 | −1 | 3 | 3\u003Cbr>2 |\n| 3 | 3 | −1 | 4 | 1 |\n| 4 | 2 | −1 | 5 | 1 |\n| 5 | 1 | 0 | 6 |  1\u003Cbr>−\u003Cbr>2 |\n| 6 | 2 | 1 | 4 | −2 |\n\nPart 1) Given h1 (x) = f (x) + g(x), find h1 ' (2)  \nPart 2) Given h2 (x) = f (x) − g(x), find h2 ' (3)  \nPart 3) Given h3 (x) = f (x) ⋅ g(x), find h3 ' (4)  \nf (x)   \nPart 4) Given h4 (x) = , find h4 ' (2)  \ng( x)  \nPart 5) Given h5 ( x) = ( f ( x))2 , find h5 ' (2)  \nPart 6) Given h6 ( x) = f ( g( x)), find h6 ' (6)  \nh 1 ' (2) = f ' (2) + g ' (2) = ~~ ~~12 h2 ' (3) = f ' (3) − g ' (3) = −2  \nh3 ' (4) = f (4) ⋅ g ' (4) + g(4) ⋅ f ' (4) = −3 g(2) ⋅ f ' (2) − f (2) ⋅ g ' (2)  \nh4 ' (2) = 2 = −1  \n( g(2)) h5 ' (2) = 2 ⋅ f (2) ⋅ f ' (2) = −8 h6 ' (6) = f ' (g(6)) ⋅ g ' (6) = 2  \nCreate your own worksheets like this one with Infinite Calculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaings33d7AUjk","https://ap.wps.com/l/cbCaings33d7AUjk","pdf",47350,"English","# Differentiation Problems\n## Problem 1: h(x)=f(x)+g(x)\n## Problem 2: h(x)=f(x)-g(x)\n## Problem 3: h(x)=f(x)·g(x)\n## Problem 4: h(x) (product expression)\n## Problem 5: h(x) (combination expression)\n## Problem 6: h(x)=f(g(x))","[{\"question\":\"What information is provided for each differentiation problem?\",\"answer\":\"Each problem provides a table of values for f(x), f'(x), g(x), and g'(x) at specific x values.\"},{\"question\":\"How do you find h'(x) when h(x)=f(x)+g(x)?\",\"answer\":\"Use the sum rule: h'(x)=f'(x)+g'(x), then substitute the tabulated derivatives at the requested x value.\"},{\"question\":\"What rule applies when h(x)=f(x)·g(x) and you need h'(x)?\",\"answer\":\"Use the product rule: h'(x)=f(x)g'(x)+g(x)f'(x), then use the table values at the specified x point.\"}]","Differentiation Rules with Tables - Part 3 - Worksheet | PDF",1791426214]