[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-571563-105":53,"doc-detail-571563-en":127},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":120,"head_meta":122,"extra_data":124,"updated_unix":126},105,"en","calculus-derivatives-and-integrals-reference-sheet","Calculus Derivatives and Integrals Reference Sheet","","This reference document provides a comprehensive compilation of fundamental calculus formulas, specifically covering essential differentiation and integration rules. It includes derivatives for basic algebraic, trigonometric, exponential, logarithmic, and inverse trigonometric functions, alongside the chain, product, and quotient rules. Furthermore, it details standard indefinite integrals, including common trigonometric and inverse trigonometric forms, designed to assist students and professionals in rapid mathematical problem-solving. This academic resource serves as a convenient cheat sheet for mastering essential calculus identities and operational techniques for both differential and integral calculus applications.",{"@graph":63,"@context":119},[64,80,102],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":51,"@type":70,"position":76},"https://docshare.wps.com/template/general/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/calculus-derivatives-and-integrals-reference-sheet/571563/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/calculus-derivatives-and-integrals-reference-sheet/571563.png","ImageObject",442,249,{"name":88,"@type":89},"Riley West","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-25","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":101},"InteractionCounter",{"@type":100},"ViewAction",8,{"@type":103,"mainEntity":104},"FAQPage",[105,111,115],{"name":106,"@type":107,"acceptedAnswer":108},"What is the derivative of the natural logarithm function ln|x|?","Question",{"text":109,"@type":110},"The derivative of ln|x| with respect to x is 1/x.","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"What is the integral of sin x dx?",{"text":114,"@type":110},"The integral of sin x dx is -cos x + C, where C is the constant of integration.",{"name":116,"@type":107,"acceptedAnswer":117},"How is the derivative of a product of two functions calculated?",{"text":118,"@type":110},"The derivative of the product f(x)g(x) is given by the product rule: f(x)g'(x) + g(x)f'(x).","https://schema.org",{"og:url":78,"og:type":121,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":123,"canonical":78},"index,follow",{"doc_id":125,"site_id":56},571563,1791997450,{"code":4,"msg":5,"data":128},{"doc_id":125,"user_id":129,"nickname":88,"user_avatar":130,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":101,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":9,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":4},1099523885074,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","ddx k = 0 (1)  \nddx [f(x) 􀀆 g(x)] = f0 (x) 􀀆 g0 (x) (2)  \nddx [k 􀀁 f(x)] = k 􀀁 f0 (x) (3)  \nddx [f(x)g (x)] = f(x)g0 (x) + g(x)f 0 (x) (4) ddx 􀀒 fg~~(~~(xx~~)~~) 􀀓 = g~~ ~~(x)f~~ ~~0~~ ~~(x[g)()f]2(x)g0~~ ~~(x) (5)  \nddx f (g(x)) = f0 (g(x)) 􀀁 g0 (x) (6)  \nddx xn = nxn􀀀1 (7)  \nddx sin x = cos x (8)  \nddx cos x = 􀀀 sin x (9)  \nddx tan x = sec2 x (10)  \nddx cot x = 􀀀 csc2 x (11)  \nddx sec x = sec x tan x (12)  \nddx cscx = 􀀀 cscx cotx (13)  \nddx ex = ex (14)  \nddx ax = ax lna (15)  \nddx ln j xj = 1x (16)  \n d  sin 􀀀1 x =  1  (17)  \ndx p 1 􀀀 x2  \n d  cos 􀀀1 x =  􀀀1  (18)  \ndx p 1 􀀀 x2  \nddx tan􀀀1 x = x2~~ ~~ (19)  \nddx cot 􀀀1 x = x2􀀀~~ 1~~ (20)  \n d  1  \nsec 􀀀1 x = ~~  ~~ (21)  \ndx j xj px2 􀀀 1  \nddx csc 􀀀1 x = jxj~~ ~~p12~~ ~~􀀀~~ 1~~ (22)  \nZ dx = x + C (1)  \nZ xn dx = xn1~~1~~ + C (2)  \nZ dxx = ln jxj + C (3)  \nZ ex dx = ex + C (4)  \nZ ax dx = ~~l~~1~~n~~aax + C (5) Z lnxdx = xlnx 􀀀 x + C (6)  \nZ sin x dx = 􀀀 cos x + C (7)  \nZ cos x dx = sin x + C (8)  \nZ tan x dx = 􀀀 ln j cos xj + C (9)  \nZ cotx dx = ln j sin xj + C (10) Z sec x dx = ln j sec x + tan xj + C (11) Z cscxdx = 􀀀 ln j csc x + cot xj + C (12)  \nZ sec2 x dx = tan x + C (13) Z csc2 x dx = 􀀀 cotx + C (14)  \nZ sec x tan x dx = sec x + C (15) Z cscx cotx dx = 􀀀 cscx + C (16)  \nZ pad2~~ ~~x2 = sin􀀀1 xa + C (17)  \nZ a2~~ ~~x2 = 1a tan􀀀1 xa + C (18)  \nZ xpdx2x􀀀~~ ~~a2 = 1a sec 􀀀1 j~~ ~~xaj + C (19)","cbCaiatfn1cyM8ix","https://ap.wps.com/l/cbCaiatfn1cyM8ix","pdf",34377,"English","# Differentiation Formulas\n## Integration Formulas","[{\"question\":\"What is the derivative of the natural logarithm function ln|x|?\",\"answer\":\"The derivative of ln|x| with respect to x is 1/x.\"},{\"question\":\"What is the integral of sin x dx?\",\"answer\":\"The integral of sin x dx is -cos x + C, where C is the constant of integration.\"},{\"question\":\"How is the derivative of a product of two functions calculated?\",\"answer\":\"The derivative of the product f(x)g(x) is given by the product rule: f(x)g'(x) + g(x)f'(x).\"}]","Calculus Derivatives and Integrals Reference Sheet | PDF",1791922371]