[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-572893-105":3,"detail-sidebar-cat-1-en-105":81,"doc-detail-572893-en":126},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","math-1310-004-the-final-cheat-sheet-calculus-reference-guide","Math 1310-004 The Final Cheat Sheet - Calculus Reference Guide","","This document serves as a comprehensive final cheat sheet for the Math 1310-004 calculus course, providing essential formulas and rules for differentiation and integration. It covers foundational concepts including rules for differentiating combinations of functions, integration by substitution and parts, and a detailed table of antiderivatives and derivatives for various functions such as polynomials, exponentials, and trigonometric functions. Furthermore, the guide includes fundamental trigonometric identities, laws of exponents, logarithmic properties, and the formula for linear approximations of a function. Designed for quick review, this reference tool helps students organize and access key mathematical principles required for successful completion of final examinations in calculus. Its structured layout enables efficient verification of identities and derivative operations during study sessions.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/template/","Template",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/template/general/","General",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/template/math-1310-004-the-final-cheat-sheet-calculus-reference-guide/572893/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/math-1310-004-the-final-cheat-sheet-calculus-reference-guide/572893.png","ImageObject",442,249,{"name":42,"@type":43},"Maya Linwood","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-19","2026-10-13",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",5,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the formula for the linear approximation of f(b) given f(a) and f'(a)?","Question",{"text":63,"@type":64},"The linear approximation is given by La(b) = f(a) + f'(a)(b - a), which is used for values of b near a.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How are exponents combined using multiplication and division?",{"text":68,"@type":64},"Exponents follow the rules cx * cy = cx+y and cx/cy = cx-y. Additionally, logarithmic properties allow logs of products to be expanded as the sum of individual logs: log(xy) = log(x) + log(y).",{"name":70,"@type":61,"acceptedAnswer":71},"What are the two primary integration techniques listed?",{"text":72,"@type":64},"The document outlines integration by substitution, where ∫f(g(x))g'(x)dx = ∫f(u)du, and integration by parts, defined by ∫u dv = uv - ∫v du.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},572893,1792011645,{"code":4,"msg":82,"data":83},"success",[84,89,94,99,104,109,114,119,123],{"id":85,"doc_module":22,"doc_module_name":25,"category_name":86,"show_sort_weight":87,"slug":88},11,"Presentations",90,"presentations",{"id":90,"doc_module":22,"doc_module_name":25,"category_name":91,"show_sort_weight":92,"slug":93},12,"Resumes",80,"resumes",{"id":95,"doc_module":22,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},14,"Invoices",70,"invoices",{"id":100,"doc_module":22,"doc_module_name":25,"category_name":101,"show_sort_weight":102,"slug":103},15,"Posters",60,"posters",{"id":105,"doc_module":22,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},16,"Social Media",50,"social-media",{"id":110,"doc_module":22,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},17,"Forms",40,"forms",{"id":115,"doc_module":22,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},18,"Letters",30,"letters",{"id":120,"doc_module":22,"doc_module_name":25,"category_name":121,"show_sort_weight":55,"slug":122},21,"Paper Templates","papers-templates",{"id":124,"doc_module":22,"doc_module_name":25,"category_name":29,"show_sort_weight":4,"slug":125},158,"general-158",{"code":4,"msg":82,"data":127},{"doc_id":79,"user_id":128,"nickname":42,"user_avatar":129,"doc_module":22,"category_id":124,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":22,"language":135,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":12,"update_tm":139,"read_time":4},962084928432,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Math 1310-004 The Final Cheat Sheet  \nRules for Di􀀋erentiating Combinations of Functions.  \n(cf )0 = cf0 ; (f + g)0 = f0 + g0 ; (f 􀀀 g)0 = f0 􀀀 g0  \nf 0g 􀀀 fg0  \n(fg)0 = f0g + fg0 ; (f =g)0 = g 2 ; f (g(x))0 = f0 (g(x)) 􀀁 g0 (x)  \nTwo Integration Techniques  \nZ f (g(x))g0 (x)dx = Z f (u)du; u = g(x); du = g0 (x)dx Z f (x)g0 (x)dx = f(x)g (x) 􀀀 Z f 0 (x)g (x)dx Z u dv = uv 􀀀 Z v du u = f(x); dv = g0 (x)dx; du = f0 (x)dx; v = g(x)  \nSome Antiderivatives/Functions/Derivatives.  \nR f (x)dx C  \nn1 xn+1 + C ln(x) + C ex + C  \n􀀐 ln~~1~~(a) 􀀑 ax + C  \n􀀀 cos(x) + C sin(x) + C  \nln(j sec(x)j) + C  \nln(j sec(x) + tan(x)j) + C? + C? + C  \nf (x)  \n0 (n  􀀀1) xnx􀀀1  \nex (a > 0 ;  1) ax sin(x)  \ncos(x)  \ntan(x) sec(x)  \ntan􀀀1(x)  \nsin􀀀1 (x)  \nf 0 (x) 0  \nnxn􀀀1  \n􀀀x􀀀2  \nex (ln(a))ax cos(x)  \n􀀀 sin(x)  \nsec2 (x) sec(x) tan(x)  \n1  \n1+x2  \n 1   \np 1􀀀x2  \nTwo Trig Identities. sin2 (x) + cos2 (x) = 1 ; tan2 (x) + 1 = sec2 (x) [Exponents.](Exponents. cx)[ c](Exponents. cx)[x](Exponents. cx)+y = cx cy ; c􀀀x = 1=cx ; (cx )y = cxy ; bxcx = (bc)x Logs. log(xy) = log(x) + log(y) ; log(xy ) = y log(x)  \nlog(x=y) = log(x) 􀀀 log(y) ; logb (x) = ln(x)= ln(b)  \nMiscellaneous: f (x)g (x) = eg (x) ln(f(x)) and ~~d~~dx ln(f(x)) = ff0((xx)) Linear Approximations: Given f (a) and f 0 (a), then:  \nLa (b) = f(a) + f0 (a)(b 􀀀 a)  \nis the linear approximation of f(b) for b \\near\" a.","cbCaiedifBgFnOsc","https://ap.wps.com/l/cbCaiedifBgFnOsc","pdf",103872,"English","# Differentiation and Integration Rules\n## Differentiation of Combined Functions\n## Integration Techniques\n# Mathematical Tables and Identities\n## Antiderivatives and Derivatives\n## Trigonometric Identities\n# Algebraic and Miscellaneous Formulas\n## Laws of Exponents\n## Logarithmic Properties\n## Linear Approximations","[{\"question\":\"What is the formula for the linear approximation of f(b) given f(a) and f'(a)?\",\"answer\":\"The linear approximation is given by La(b) = f(a) + f'(a)(b - a), which is used for values of b near a.\"},{\"question\":\"How are exponents combined using multiplication and division?\",\"answer\":\"Exponents follow the rules cx * cy = cx+y and cx/cy = cx-y. Additionally, logarithmic properties allow logs of products to be expanded as the sum of individual logs: log(xy) = log(x) + log(y).\"},{\"question\":\"What are the two primary integration techniques listed?\",\"answer\":\"The document outlines integration by substitution, where ∫f(g(x))g'(x)dx = ∫f(u)du, and integration by parts, defined by ∫u dv = uv - ∫v du.\"}]","Math 1310-004 The Final Cheat Sheet - Calculus Reference Guide | PDF",1791929915]