[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-572652-105":53,"doc-detail-572652-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","table-of-derivatives-82","Table of Derivatives - 8.2","","This educational leaflet provides a comprehensive table of common mathematical functions and their corresponding derivatives. Designed as a quick reference for students and learners, the document covers elementary algebraic powers, exponential functions, logarithmic functions, trigonometric functions, and hyperbolic functions. It includes a structured table for easy lookup and a set of practice exercises with detailed answers to facilitate the mastery of differentiation rules. The material serves as an essential resource for those studying introductory calculus and mathematics-related fields. By offering clear examples of how to apply these rules to various variables, the leaflet ensures that learners can effectively find the derivative of diverse functional expressions.",{"@graph":63,"@context":122},[64,80,101],{"@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/table-of-derivatives-82/572652/",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/table-of-derivatives-82/572652.png","ImageObject",442,249,{"name":88,"@type":89},"Supernature","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-20","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":47},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114,118],{"name":105,"@type":106,"acceptedAnswer":107},"What is the derivative of an exponential function e^(kx)?","Question",{"text":108,"@type":109},"The derivative of e^(kx) with respect to x is k*e^(kx).","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"How do you find the derivative of a constant k?",{"text":113,"@type":109},"The derivative of any constant k with respect to x is always 0.",{"name":115,"@type":106,"acceptedAnswer":116},"What is the derivative of tan x?",{"text":117,"@type":109},"The derivative of tan x is sec^2 x.",{"name":119,"@type":106,"acceptedAnswer":120},"How is the derivative of x^n calculated?",{"text":121,"@type":109},"The derivative of x^n with respect to x is n*x^(n-1), where n is any constant.","https://schema.org",{"og:url":78,"og:type":124,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":126,"canonical":78},"index,follow",{"doc_id":128,"site_id":56},572652,1792009230,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":88,"user_avatar":133,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":47,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":73,"language":139,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":61,"update_tm":143,"read_time":9},962093270004,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","8.2  \nTable of derivatives  \nIntroduction  \nThis leaflet provides a table of common functions and their derivatives.  \n1 . The table of derivatives  \n\n| y = f(x) | d~~y~~dx = f′(x) |\n| --- | --- |\n| k, any constant | 0 |\n| x | 1 |\n| x2 | 2x |\n| x3 | 3x2 |\n| xn , any constant n | nxn−1 |\n| ex | ex |\n| ekx | kekx |\n| ln x = loge x | 1 x |\n| sin x | cos x |\n| sinkx | k cos kx |\n| cos x | − sin x |\n| coskx | −k sinkx |\n| tan x = scinos~~x~~x | sec2 x |\n| tankx | k sec2 kx |\n| cosec x = si1nx | −cosec x cot x |\n| sec x = co1sx | sec x tan x |\n| cotx = csosin~~x~~x sin −1 x cos −1 x tan−1 x | −cosec2 x 1\u003Cbr>√ 1−x2  −1 \u003Cbr>√ 1−x2  1  1+x2 |\n| cosh x | sinh x |\n| sinh x | coshx |\n| tanhx | sech2 x |\n| sechx | −sechx tanhx |\n| cosech x | −cosech x cothx |\n| cothx | −cosech2 x |\n| cosh −1 x\u003Cbr>sinh −1 x\u003Cbr>tanh−1 x | 1\u003Cbr>√x2 −1  1 \u003Cbr>√x2 +1  1  1−x2 |\n\n[www.mathcentre.ac.uk](www.mathcentre.ac.uk)  \n8.2.1  \n􀀍c Pearson Education Ltd 2000  \nExercises  \n1. In each case, use the table of derivatives to write down dy  \ndx .  \na) y = 8  \nb) y = −2  \nc) y = 0  \nd) y = x  \ne) y = x5  \nf) y = x7  \ng) y = x−3  \nh) y = x1/2  \ni) y = x−1/2  \nj) y = sin x  \nk) y = cos x  \nl) y = sin4x  \nm) y = cos 12x  \nn) y = e4x  \no) y = ex  \np) y = e−2x  \nq) y = e−x  \nr) y = ln x  \ns) y = logex  \nt) y = √x  \nu) y = √3 x  \nv) y = x  \nw) y = ex/2  \ndy  \n2. You should be able to use the table when other variables are used. Find if  \ndt  \na) y = e7t , b) y = t4 , c) y = t−1 , d) y = sin 3t.  \nAnswers  \n1. a) 0, b) 0, c) 0, d) 1, e) 5x4 , f) 7x6 , g) −3x−4, h) 12x−1/2, i) − 12x−3/2, j) cos x, k) −sin x, l) 4 cos4x, m) − 12 sin 12x, n) 4e4x, o) ex , p) −2e−2x, q) −e−x, r) 1x, s) 1xt) 12x−1/2 = 2x11/2 = 2x , u) 13x−2/3 = 3x12/3 = 3x2 , v) − 12x−3/2, w) 12ex/2 .  \n2. a) 7e7t, b) 4t3 , c) − t12 , d) 3 cos3t.  \n[www.mathcentre.ac.uk](www.mathcentre.ac.uk)  \n8.2.2  \n􀀍c Pearson Education Ltd 2000","cbCaijxh6GgHuZ4i","https://ap.wps.com/l/cbCaijxh6GgHuZ4i","pdf",98050,"English","# Table of derivatives\n# Exercises\n## Practice problems\n## Solutions","[{\"question\":\"What is the derivative of an exponential function e^(kx)?\",\"answer\":\"The derivative of e^(kx) with respect to x is k*e^(kx).\"},{\"question\":\"How do you find the derivative of a constant k?\",\"answer\":\"The derivative of any constant k with respect to x is always 0.\"},{\"question\":\"What is the derivative of tan x?\",\"answer\":\"The derivative of tan x is sec^2 x.\"},{\"question\":\"How is the derivative of x^n calculated?\",\"answer\":\"The derivative of x^n with respect to x is n*x^(n-1), where n is any constant.\"}]","Table of Derivatives - 8.2 | PDF",1791928693]