[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-571480-105":53,"doc-detail-571480-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","common-derivatives-and-integrals-basic-formulas","Common Derivatives and Integrals - Basic Formulas","","A concise calculus reference compiling common derivative and integral formulas alongside core rules for differentiation. It covers fundamental properties such as linearity, product and quotient rules, and the chain rule, then lists frequent derivative results for polynomials, trigonometric, inverse trigonometric, exponential/logarithmic, and hyperbolic functions. The integrals section provides standard antiderivative rules across the same function families and highlights selection criteria for special cases. It also summarizes integration techniques like u-substitution and integration by parts, plus trig substitutions and partial fractions.",{"@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":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/common-derivatives-and-integrals-basic-formulas/571480/",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/common-derivatives-and-integrals-basic-formulas/571480.png","ImageObject",442,249,{"name":88,"@type":89},"SundayMiles","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-21","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":101},"InteractionCounter",{"@type":100},"ViewAction",7,{"@type":103,"mainEntity":104},"FAQPage",[105,111,115],{"name":106,"@type":107,"acceptedAnswer":108},"What are the basic differentiation rules included in the reference?","Question",{"text":109,"@type":110},"The document lists linearity, the product rule, the quotient rule, and the chain rule, using standard derivative notation and examples.","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"Which types of functions have common derivative formulas?",{"text":114,"@type":110},"It provides common derivatives for polynomials, trigonometric functions, inverse trigonometric functions, exponential/logarithmic functions, and hyperbolic trigonometric functions.",{"name":116,"@type":107,"acceptedAnswer":117},"What integration techniques are summarized beyond basic antiderivative formulas?",{"text":118,"@type":110},"It includes u-substitution and integration by parts, and it also introduces trig substitutions and partial fractions as standard integration techniques.","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},571480,1792022810,{"code":4,"msg":5,"data":128},{"doc_id":125,"user_id":129,"nickname":88,"user_avatar":130,"doc_module":9,"category_id":8,"category_name":11,"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":79,"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":73},1099529839202,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Common Derivatives and Integrals  \nDerivatives  \nBasic Properties/Formulas/Rules  \nddx~~ ~~ ( cf ( x )) = cf ¢ (x ) , c is any constant. ( f ( x ) ± g ( x ))¢ = f ¢ (x ) ± g¢ (x ) ddx~~ ~~ ( xn) = nxn-1 , n is any number. ~~ ~~ddx~~ ~~ ( c ) = 0 , c is any constant.  \n( f g )¢ = f ¢ g + f g ¢ –(Product Rule) ÊÁ  f ˆ˜¢ = ~~ ~~f~~ ~~¢~~ ~~g-2f~~ ~~g~~ ~~¢~~ ~~ –(Quotient Rule)  \nË g ¯ g  \nddx~~ ~~ ( f ( g ( x ))) = f ¢ (g ( x ))g ¢ (x ) (Chain Rule)  \nddx~~ ~~ (eg (x ) ) = g ¢ (x ) eg (x ) ~~ ~~ddx~~ ~~ (ln g ( x )) = ~~ ~~gg¢~~(~~(xx~~)~~)  \nCommon Derivatives  \nPolynomials  \nddx~~ ~~ ( c ) = 0 ~~ ~~ddx~~ ~~ ( x ) = 1 ~~ ~~ddx~~ ~~ ( cx) = c ~~ ~~ddx~~ ~~ ( xn) = nxn-1 ~~ ~~ddx~~ ~~ ( cx n) = ncxn-1  \nTrig Functions ddx~~ ~~ ( sin x) = cos xddx~~ ~~ ( sec x) = sec x tan x  \nInverse Trig Functions ddx~~ ~~ ( sin-1 x ) = ~~ ~~-1~~  ~~  \nddx~~ ~~ ( sec-1 x ) = ~~ ~~~~ ~~1~~  ~~  \nx x2-1  \nddx~~ ~~ ( cos x) = -sin xddx~~ ~~ ( cscx) = -cscx cot x  \nddx~~ ~~ ( cos-1 x ) = - ~~ ~~-1~~  ~~  \nddx~~ ~~ ( csc-1 x ) = - ~~ ~~x~~ ~~1x-1  \nddx~~ ~~ ( tan x) = sec2 xddx~~ ~~ ( cot x) = -csc2 x  \nddx~~ ~~ ( tan-1 x ) = ~~ ~~1~~ ~~+1x2 ddx~~ ~~ ( cot-1 x ) = - ~~ ~~1~~ ~~+1x2  \nExponential/Logarithm Functions  \nddx~~ ~~ ( ax) = ax ln ( a ) ~~ ~~ddx~~ ~~ ( ex) = ex  \nddx~~ ~~ (ln ( x )) = ~~ ~~1x~~ ~~ , x > 0 ~~ ~~ddx~~ ~~ (ln x ) = ~~ ~~1x~~ ~~ , x 􀂹 0 ~~ ~~ddx~~ ~~ (loga ( x )) = ~~ ~~x~~l~~1n~~ ~~a~~ ~~ , x > 0 Hyperbolic Trig Functions  \nddx~~ ~~ ( sinh x) = cosh xddx~~ ~~ ( sech x) = -sech x tanh x  \nddx~~ ~~ ( cosh x) = sinh xddx~~ ~~ ( csch x) = -csch x coth x  \nddx~~ ~~ ( tanh x) = sech2 xddx~~ ~~ ( coth x) = -csch2 x  \nVisit [http://tutorial.math.lamar.edu](http://tutorial.math.lamar.edu) for a complete set of Calculus I & II notes. © 2005 Paul Dawkins  \nCommon Derivatives and Integrals  \nIntegrals  \nBasic Properties/Formulas/Rules  \nÚcf ( x ) dx = c Ú f ( x ) dx , c is a constant.  \nÚ baf ( x ) dx = F ( x )ba = F ( b )-F ( a ) where  \nÚ ba cf ( x ) dx = c Úba f ( x ) dx , c is a constant.  \nÚ aa f ( x ) dx = 0  \nÚ baf ( x ) dx = Ú ca f ( x ) dx + Úcb f ( x ) dx  \nÚ f ( x ) ± g ( x ) dx = Ú f ( x ) dx ± Ú g ( x ) dx F ( x ) = Ú f ( x ) dx  \nÚ ba f ( x ) ± g ( x ) dx = Ú ba f ( x ) dx ± Ú ba g ( x ) dx  \nÚ baf ( x ) dx = - Úba f ( x ) dx  \nÚ bac dx = c ( b-a )  \nIf f ( x ) 􀂳 0 on a £ x £ b then Úbaf ( x ) dx 􀂳 0  \nIf f ( x ) 􀂳 g ( x ) on a £ x £ b then Úbaf ( x ) dx 􀂳 Ú ba g ( x ) dx  \nCommon Integrals  \nPolynomials  \nÚ dx = x + c Ú k dx = k x + c Úxn dx = ~~ ~~n~~ ~~~~ ~~1 xn+1 + c, n 􀂹 -1  \nıÛÙ ~~ ~~1x~~ ~~ dx = ln x  + c Úx-1 dx = ln x  + c Úx-ndx = ~~ ~~-n1+1 x-n+1 + c, n 􀂹 1  \nıÛÙ ~~ ~~ax~~ ~~b~~ ~~ dx = ~~ ~~1a~~ ~~ ln ax + b + c Úxpqdx = ~~  ~~pq~~ ~~~~ ~~1 x ~~ ~~pq+1 + c = ~~ ~~p~~ ~~~~ ~~q~~ ~~ xp+qq + c  \nTrig Functions  \nÚcosu du = sin u + c  \nÚsecu tan u du = sec u + c  \nÚsin u du = -cosu + c  \nÚcscu cotudu = -cscu + c  \nÚsec2 u du = tan u + c  \nÚcsc2 u du = -cot u + c  \nÚ tan u du = ln sec u + c  \nÚsec u du = ln sec u + tan u + c  \nÚcscu du = ln cscu-cot u + c  \nÚcot u du = ln sin u + c  \nÚsec3 u du = ~~ ~~12 ( secu tan u + ln sec u + tan u) + c  \nÚcsc3 u du = ~~ ~~12 (-cscu cot u + ln cscu-cot u) + c  \nExponential/Logarithm Functions  \nÚeu du = eu + c Ú au du = ~~ l~~anua~~ ~~ + c  \nÚeau sin ( bu) du = ~~ ~~a2eb2~~ ~~ ( a sin ( bu)-bcos( bu)) + c  \nÚeau cos ( bu) du = ~~ ~~a~~ ~~2eb2~~ ~~ ( a cos ( bu) + b sin ( bu)) + c  \nÚ ln u du = u ln ( u ) -u + c  \nÚueu du = ( u-1) eu + c  \nıÛÙ ~~ ~~u~~ l~~1n~~ ~~u~~ ~~ du = ln ln u + c  \nVisit [http://tutorial.math.lamar.edu](http://tutorial.math.lamar.edu) for a complete set of Calculus I & II notes. © 2005 Paul Dawkins  \nCommon Derivatives and Integrals  \nInverse Trig Functions  \nıÙÛ ~~ ~~1~~  ~~ du = sin-1 ËÁÊ ~~ ~~uaˆ¯˜ + c  \nÛ 1 1 -1 Ê u ˆ  \nıÙ  a 2 + u 2  du = ~~ ~~a~~ ~~ tan ËÁ ~~ ~~a~~ ~~ ¯˜ + c  \nÛ 1 1 -1 Ê u ˆ  \nıÙ  u   du = ~~ ~~a~~ ~~ sec ËÁ ~~ ~~a~~ ~~ ¯˜ + c  \nÚsin-1u du = u sin-1 u +  + c  \nÚ tan-1u du = u tan-1 u- ~~ ~~12~~ ~~  ln ( 1+ u 2 ) + c  \nÚcos-1u du = u cos-","cbCaitthLy8oRaol","https://ap.wps.com/l/cbCaitthLy8oRaol","pdf",142906,"English","# Derivatives\n## Basic Properties/Formulas/Rules\n## Common Derivatives\n# Integrals\n## Basic Properties/Formulas/Rules\n## Common Integrals\n# Standard Integration Techniques\n## u Substitution\n## Integration by Parts\n## Trig Substitutions\n## Partial Fractions","[{\"question\":\"What are the basic differentiation rules included in the reference?\",\"answer\":\"The document lists linearity, the product rule, the quotient rule, and the chain rule, using standard derivative notation and examples.\"},{\"question\":\"Which types of functions have common derivative formulas?\",\"answer\":\"It provides common derivatives for polynomials, trigonometric functions, inverse trigonometric functions, exponential/logarithmic functions, and hyperbolic trigonometric functions.\"},{\"question\":\"What integration techniques are summarized beyond basic antiderivative formulas?\",\"answer\":\"It includes u-substitution and integration by parts, and it also introduces trig substitutions and partial fractions as standard integration techniques.\"}]","Common Derivatives and Integrals - Basic Formulas | PDF",1791919925]