[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-571644-105":53,"doc-detail-571644-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-summary-formulas-differentiation-formulas-trigonometric-and-integration-formulas","Calculus Summary Formulas - Differentiation Formulas - Trigonometric and Integration Formulas","","Calculus Summary Formulas provides a compact reference of core differentiation rules, including product/quotient/chain rule forms and derivatives of common functions such as powers, exponentials, logarithms, and trigonometric functions. It also lists major trigonometric identities and integration results, including definitions and examples for improper integrals, standard antiderivatives, and key evaluation forms. The sheet further summarizes foundational limit, continuity, and theorem statements such as limits of rational functions, intermediate value, Rolle’s, mean value, and extreme-value theorems.",{"@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/calculus-summary-formulas-differentiation-formulas-trigonometric-and-integration-formulas/571644/",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-summary-formulas-differentiation-formulas-trigonometric-and-integration-formulas/571644.png","ImageObject",442,249,{"name":88,"@type":89},"Marglet","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-22","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},"Which differentiation rules are included for typical composite functions?","Question",{"text":109,"@type":110},"The document includes differentiation formulas for common cases and the chain rule form, along with basic power, exponential, and logarithmic derivatives. It also lists structured derivative results for trigonometric functions.","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"What trigonometric identities are listed for simplification?",{"text":114,"@type":110},"It provides fundamental identities such as sin²θ + cos²θ = 1, relations involving tan, sec, cot, and csc, plus sum and difference formulas for sine and cosine. It also includes double-angle identities.",{"name":116,"@type":107,"acceptedAnswer":117},"Which calculus theorems about limits and function behavior are summarized?",{"text":118,"@type":110},"It summarizes definitions and criteria for limits and continuity, the intermediate-value theorem, and results like Rolle’s theorem, mean value theorem, and the extreme-value theorem with guidance on where maxima/minima can occur.","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},571644,1792360248,{"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":47,"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},2336477982702,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","CSSS 505  \nCalculus Summary Formulas  \nDifferentiation Formulas  \n1.  d  (x n ) = nx n−1 17. dy = dy  ×  du  Chain Ruledx dx dx dx  \n2. ~~ ~~ddx~~ ~~ ( fg) = fg ′ + gf ′  \n3.  d  ( f ) = ~~ ~~gf~~ ~~′~~ ~~−2~~ ~~fg~~ ~~′ dx g g  \n4. ~~ ~~ddx~~ ~~ f (g (x)) = f ′(g (x))g ′(x)  \n5. ~~ ~~ddx~~ ~~ (sin x) = cos x  \n6. ~~ ~~ddx~~ ~~ (cos x) = − sin x  \n7. ~~ ~~ddx~~ ~~ (tan x) = sec 2 x  \n8. ~~ ~~ddx~~ ~~ (cot x) = − csc2 x  \n9. ~~ ~~ddx~~ ~~ (sec x) = sec x tan x  \n10. ddx~~ ~~ (cscx) = − cscx cot x  \n11. ddx~~ ~~ (ex ) = ex  \n12. ddx~~ ~~ (a x ) = a x ln a  \n13. ddx~~ ~~ (ln x) = 1x  \n14.  d  (Arc sin x) = 1 dx  1 − x 2   \n15. ddx~~ ~~ (Arc tan x) = 1~~ ~~+1x~~ ~~2~~ ~~  \n16.  d  (Arcsec x) = 1 dx | x |  x 2 −1  \nTrigonometric Formulas  \n1. sin 2 θ + cos 2 θ = 1 13. tan θ =  sinθ =  1   \n2. 1 + tan 2 θ = sec 2 θ cos θ cot θ  \n3. 1 + cot 2 θ = csc 2 θ 14. cot θ =  cos θ =  1  4. sin(−θ ) = − sinθ sinθ tan θ 56.. costan((−θθ))  ostaθ 15. sec θ = ~~ ~~co1s~~θ~~  \n7. sin(A + B) = sin AcosB + sin B cosA 16 csc θ =  1   \n8. sin(A − B) = sin AcosB − sin B cosA . sinθ  \n9. cos(A + B) = cos A cos B − sin AsinB 17. cos(~~ ~~π2~~ ~~ −θ ) = sinθ  \n10. cos(A − B) = cosA cos B + sin AsinB 18. sin(~~ ~~π2~~ ~~ −θ ) = cos θ  \n11. sin 2θ = 2 sinθcos θ  \n12. cos 2θ = cos 2 θ − sin 2 θ = 2 cos 2 θ −1 = 1 − 2sin 2 θ  \nIntegration Formulas  \nDefinition of a Improper Integral  \nb  \n∫ f (x) dx is an improper integral ifa  \n1. f becomes infinite at one or more points of the interval of integration, or  \n2. one or both of the limits of integration is infinite, or  \n3. both (1) and (2) hold.  \n1. ∫a dx = ax + C  \n2. ∫x n dx = xn11 + C, n ≠ −1  \n3. ∫ ~~ ~~1x~~ ~~ dx = ln x + C  \n4. ∫ex dx = ex + C  \n5. ∫a x dx = lanxa + C  \n6. ∫ ln x dx = x ln x − x + C  \n7. ∫ sin x dx = − cos x + C  \n8. ∫ cos x dx = sin x + C  \n9. ∫ tan x dx = ln sec x + C or − lncos x + C  \n10. ∫ cot x dx = ln sin x + C  \n11. ∫ sec x dx = ln sec x + tan x + C  \n12. ∫ cscx dx = ln cscx − cot x + C  \n13. ∫ sec 2 x dx = tan x + C  \n14. ∫ sec x tan x dx = sec x + C  \n15. ∫ csc 2 x dx = − cot x + C  \n16. ∫ cscx cot x dx = − cscx + C  \n17. ∫ tan 2 x dx = tan x − x + C  \n18. ∫ ~~ ~~a~~ ~~2~~ ~~x~~ ~~2~~ ~~ = ~~ ~~1a~~ ~~ Arc tan􀂨􀂧􀂩 ~~ ~~xa~~ ~~ 􀂷􀂹􀂸 + C  \n19. ∫ d2 = Arc sin 􀂧􀂩􀂨 xa~~ ~~ 􀂷􀂹􀂸 + C  \n20. ∫ d2x− = 1a~~ ~~ Arcsec xa + C = 1a~~ ~~ Arc cos  \na  \nx  \n+ C  \nFormulas and Theorems  \n1a.  Definition of Limit: Let f be a function defined on an open interval containing c (except possibly at c ) and let L be a real number. Then lim f (x) = L means that for each ε > 0 there  \nx → a  \nExample  \nExample  \nExample  \ng nge  \nAverage of Change  \nof g  \nexists a δ > 0 such that f (x) − L \u003C ε whenever 0 \u003C x − c \u003C δ . 1b. A function y = f (x) is continuous at x = a if  \ni) . f(a) exists  \nii) . lim f (x) exists  \nx → a  \niii) . lim = f (a)  \nx → a  \n4. Intermediate-Value Theorem  \nA function y = f (x) that is continuous on a closed interval [a, b] takes on every value between f (a) and f (b) .  \nNote: If f is continuous on [a, b] and f (a) and f (b) differ in sign, then the equation  \nf (x) = 0 has at least one solution in the open interval (a, b) .  \n5. Limits of Rational Functions as x → ±∞  \ni) . x ∞ fg((xx)) = 0 if the degree of f (x) \u003C the degree of g (x)  \n2  \n: lim x − 2x = 0  \nx → ∞ x 3 + 3  \nii) . lim f (x) is infinite if the degrees of f (x) > the degree of g (x)  \nx→±∞ g (x)  \n3  \n: lim x 2+ 2x = ∞  \nx → ∞ x − 8  \niii) . lim f (x) is finite if the degree of f (x) = the degree of g (x)  \nx→±∞ g (x)  \n2  \n: lim 2x − 3x + 2 = − 2  \nx → ∞ 10x − 5x2 5  \n6. Avera e and Instantaneous Rate of  \ni) . Rate :  \nCha  \nIf (x0 , y0 ) and (x1 , y1 ) are points on the graph of  \ny = f (x) , then the average rate of change of y with respect to  \n[x0 , x1 ] is  \nf (x1 ) − f (x0 ) y1 − y0 =  \nx1 − x0 x1 − x0  \n∆y =  \n∆x .  \nx over the interval  \nii) . Instantaneous Rate Chan e: If (x0 , y 0 ) is a point on the graph of y = f (x) , then the instantaneous rate of change of y with respect to x at x0 is f ′(x0 ) .  ","cbCaivYc0ghRkK6L","https://ap.wps.com/l/cbCaivYc0ghRkK6L","pdf",192932,"English","# Differentiation Formulas\n## Trigonometric Formulas\n## Integration Formulas\n## Formulas and Theorems","[{\"question\":\"Which differentiation rules are included for typical composite functions?\",\"answer\":\"The document includes differentiation formulas for common cases and the chain rule form, along with basic power, exponential, and logarithmic derivatives. It also lists structured derivative results for trigonometric functions.\"},{\"question\":\"What trigonometric identities are listed for simplification?\",\"answer\":\"It provides fundamental identities such as sin²θ + cos²θ = 1, relations involving tan, sec, cot, and csc, plus sum and difference formulas for sine and cosine. It also includes double-angle identities.\"},{\"question\":\"Which calculus theorems about limits and function behavior are summarized?\",\"answer\":\"It summarizes definitions and criteria for limits and continuity, the intermediate-value theorem, and results like Rolle’s theorem, mean value theorem, and the extreme-value theorem with guidance on where maxima/minima can occur.\"}]","Calculus Summary Formulas - Differentiation Formulas - Trigonometric and Integration Formulas | PDF",1791922907]