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The integration section mirrors this structure with fundamental properties, common integral formulas, and standard techniques such as u-substitution, integration by parts, trig substitutions, and partial 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are the basic rules covered for derivatives?","Question",{"text":63,"@type":64},"The document lists linearity-related derivative properties plus the constant rule and power rule, and it includes the product rule, quotient rule, and chain rule.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Which function categories have common derivative formulas?",{"text":68,"@type":64},"It provides common derivatives for polynomials, trigonometric functions, inverse trigonometric functions, exponential and logarithm functions, and hyperbolic functions.",{"name":70,"@type":61,"acceptedAnswer":71},"What integration techniques are included in the standard methods section?",{"text":72,"@type":64},"It includes u-substitution (with the mapping for changing variables), integration by parts, trig substitutions for root-containing integrals, and partial fractions for rational expressions.","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},571591,1792009231,{"code":4,"msg":82,"data":83},"success",[84,89,94,99,104,109,114,119,124],{"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 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(x) g (x) + f(x) g0 (x)– Product Rule ~~ ~~ddx 􀀐 eg(x)􀀑 = g0 (x)eg(x)  \n􀀒 fg((xx)) 􀀓 0 = f0~~ ~~(x)~~ ~~g~~ ~~(x􀀐g)~~ ~~()f􀀑(2x)~~ ~~g0~~ ~~(x)– Quotient Rule ~~ ~~ddx 􀀔 ln (g(x))􀀕 = gg0((xx)) ddx 􀀔f 􀀐g (x)􀀑􀀕 = f0 􀀐g (x)􀀑 g0 (x)– Chain Rule  \nCommon Derivatives  \nPolynomials  \nddx 􀀐 c􀀑 = 0 ~~ ~~ddx (x) = 1 ~~ ~~ddx 􀀐 cx􀀑 = c ~~ ~~ddx 􀀐xn􀀑 = nxn􀀀1 ~~ ~~ddx 􀀐 cxn􀀑 = ncxn􀀀1 Trig Functions  \nddx h sin (x)i = cos (x) ~~ ~~ddx h cos (x)i = 􀀀 sin(x) ~~ ~~ddx h tan (x)i = sec2 (x)  \nddx h csc (x)i = 􀀀 csc(x) cot (x) ~~ ~~ddx h sec (x)i = sec (x) tan (x) ~~ ~~ddx h cot (x)i = 􀀀 csc2 (x) Inverse Trig Functions  \nddx h sin􀀀1(x)i = p~~ ~~1~~ ~~~~ ~~x2~~ ~~ ~~ ~~ddx h cos􀀀1(x)i = 􀀀 p~~ ~~1~~ ~~~~ ~~x2~~ ~~ ~~ ~~ddx h tan􀀀1(x)i = 1~~ ~~x2 ddx h csc􀀀1(x)i = 􀀀 ~~ ~~jxj~~ ~~p1x2~~ ~~􀀀~~ ~~1 ~~ ~~ddx h sec􀀀1(x)i = jxj~~ ~~p1x2~~ ~~􀀀~~ ~~1 ~~ ~~ddx h cot􀀀1(x)i = 􀀀 ~~ ~~1~~ ~~x2 Exponential & Logarithm Functions  \nddx haxi = ax ln(a) ~~ ~~ddx hexi = ex  \nddx h ln (x)i = 1x ; x > 0 ~~ ~~ddx h ln j xji = 1x ; x  0 ~~ ~~ddx h loga(x)i = x~~ ~~l1n(a) ; x > 0 Hyperbolic Functions  \nddx hsinh (x)i = cosh (x) ~~ ~~ddx hcosh (x)i = sinh (x) ~~ ~~ddx htanh (x)i = sech2 (x) ddx hcsch (x)i = 􀀀 csch(x) coth (x) ~~ ~~ddx hsech (x)i = 􀀀 sech(x) tanh (x) ~~ ~~ddx hcoth (x)i = 􀀀 csch2 (x)  \n© October 2025 Paul Dawkins-[https://tutorial.math.lamar.edu](https://tutorial.math.lamar.edu)  \nIntegrals  \nBasic Properties/Formulas/Rules  \nZ cf (x) dx = c Z f (x) dx, c is a constant. Z f (x) 􀀆 g(x) dx = Z f (x)dx 􀀆 Z g (x) dx Zab f (x) dx = F (x)􀀌 ba = F (b) 􀀀 F(a) where F(x) = Z f (x) dx  \nZab cf (x) dx = c Zab f (x) dx, c is a constant. Zaa f (x)dx = 0  \nZab f (x) dx = Zac f (x) dx + Zcb f (x) dx  \nZab f (x) 􀀆 g(x) dx = Zab f (x) dx 􀀆 Zab g (x) dx Zab f (x) dx = 􀀀 Zb a f (x) dx  \nZab c dx = c (b 􀀀 a) , c is a constant.  \nIf f(x) 􀀕 0 on a 􀀔 x 􀀔 b then Zab f (x) dx 􀀕 0  \nIf f(x) 􀀕 g(x) on a 􀀔 x 􀀔 b then Zab f (x) dx 􀀕 Zab g (x) dx  \nCommon Integrals  \nPolynomials  \nZ dx = x + c Z k dx = kx + c Z xn dx = n~~ ~~~~ ~~1 xn+1 + c; n  􀀀1 Z 1x dx = ln jxj + c Z x􀀀1 dx = ln jxj + c Z x􀀀ndx = 􀀀n1+~~ ~~1 x􀀀n+1 + c; n  1 Z ax~~ ~~~~ ~~b dx = 1a ln jax + bj + c Z x pq dx = ~~p~~q~~ ~~~~ ~~1 x pq+1 + c = p~~ ~~~~ ~~q xp+qq + c  \nTrig Functions  \nZ cos (u) du = sin (u) + c Z sin (u) du = 􀀀 cos(u) + c Z sec2 u du = tan (u) + c Z sec (u)tan (u) du = sec (u) + c Z csc (u) cot (u) du = 􀀀 csc(u) + c Z csc2 u du = 􀀀 cot(u) + c Z tan (u) du = 􀀀 ln 􀀌 cos (u) 􀀌 +c = ln 􀀌 sec (u) 􀀌 +c Z cot (u) du = ln 􀀌 sin (u) 􀀌 +c = 􀀀 ln 􀀌 csc (u) 􀀌 +c Z sec (u) du = ln 􀀌 sec (u)+tan(u)􀀌 +c Z sec3 (u) du = 12 􀀒 sec (u) tan (u)+ln 􀀌 sec (u)+tan(u)􀀌 􀀓 +c Z csc (u) du = ln 􀀌 csc (u)􀀀cot(u)􀀌 +c Z csc3 (u) du = 12 􀀒􀀀csc(u) cot (u)+ln 􀀌 csc (u)􀀀cot(u)􀀌 􀀓 +c  \n© October 2025 Paul Dawkins-[https://tutorial.math.lamar.edu](https://tutorial.math.lamar.edu)  \nExponential & Logarithm Functions  \nZ Z  \nZ  \neu du = eu + c Z au du = lna(ua) + ceau sin(bu) du = a2eb2 􀀒 a sin(bu) 􀀀 b cos(bu)􀀓 + ceau cos(bu) du = a2eb2 􀀒 a cos(bu) + b sin(bu)􀀓 + c  \nZ Z  \nZ  \nln (u) du = u ln(u) 􀀀 u + cueu du = (u 􀀀 1)eu + c  \n 1   \nu ln(u) du = ln 􀀌 ln (u) 􀀌 + c  \nInverse Trig Functions  \nZ Z  \nZ  \npa21􀀀~~ ~~u2 du = sin􀀀1 􀀐 ua􀀑 + ca2~~ ~~~~ ~~u2 du = 1a tan􀀀1 􀀐 ua􀀑 + cupu12~~ ~~􀀀~~ ~~a2 du = 1a sec􀀀1 􀀐 ua􀀑 + c  \nZ Z  \nZ  \nsin􀀀1(u) du = u sin􀀀1(u) +p 1 􀀀 u2 + c tan􀀀1(u) du = u tan􀀀1(u) 􀀀 12 ln 􀀀1 + u2 􀀁 + c  \ncos􀀀1(u) du = u cos􀀀1(u) 􀀀p 1 􀀀 u2 + c  \nHyperbolic Functions Zsinh (u)du = cosh (u) + c Zcosh (u)du = sinh (u) + c  \nZsech (u)tanh (u)du = 􀀀 sech(u) + c Zcsch (u) coth (u)du = 􀀀 csch(u) + c  \nZsech2 (u)du = tanh (u) + c Zcsch2 (u)du = 􀀀 coth(u) + c  \nZtanh (u)du = ln 􀀀cosh(u)􀀁 + c Miscellaneous  \nZ a2~~ ~~~~ ~~u2 du = 21a ln 􀀌 uu~~ ~~~~ ~~aa 􀀌 + c  \nZ u2~~ ~~~~ ~~a2 du = 21a ln 􀀌 uu~~ ~~~~ ~~aa 􀀌 + c  \nZ Z ","cbCaidBs4nIIlSDX","https://ap.wps.com/l/cbCaidBs4nIIlSDX","pdf",181991,"English","# Derivatives\n## Basic Properties, Formulas, and Rules\n## Common Derivatives\n## Integration\n## Basic Properties, Formulas, and Rules\n## Common Integrals\n## Standard Integration Techniques\n## Trig Substitutions and Partial Fractions","[{\"question\":\"What are the basic rules covered for derivatives?\",\"answer\":\"The document lists linearity-related derivative properties plus the constant rule and power rule, and it includes the product rule, quotient rule, and chain rule.\"},{\"question\":\"Which function categories have common derivative formulas?\",\"answer\":\"It provides common derivatives for polynomials, trigonometric functions, inverse trigonometric functions, exponential and logarithm functions, and hyperbolic functions.\"},{\"question\":\"What integration techniques are included in the standard methods section?\",\"answer\":\"It includes u-substitution (with the mapping for changing variables), integration by parts, trig substitutions for root-containing integrals, and partial fractions for rational expressions.\"}]","Derivatives - Basic Properties/Formulas/Rules | PDF",1791922528]