Calculus Final Exam Review Nelson39;s 5 Star Stables Home微分期末考试复习尼尔森的5星级的马厩里

1、calculus final exam reviewby: bryant nelsoncommon trigonometric valuesx-value0/6/3 /22/35/67/64/33/25/311/62sin(x)01 0- -1- 0cos(x)1 0- -1- 0 1special trigonometric limitslimh0sin(h) h= ?1limh0cos(h) - 1 h= ?0differentiation rulesdefinition of a derivative:f(x) = limx0f(x+x) f(x) xdifferentiation ru

2、les cont.product rule:(fg) = fg + fgquotient rule:(f/g) = (fg - fg)/g2natural log rule:d/dx(ln(u) = (1/u)du/dxexponential rules:d/dx(u) = (u)du/dxd/dx(bu) = (bu) ln(b)du/dxdifferentiation rules cont. d/dx(sin(u) =(cos(u)du/dxtrigonometric rulesd/dx(cos(u) =(-sin(u)du/dxd/dx(tan(u) =(sec2(u)du/dxd/dx

3、(cot(u) =(-csc2(u)du/dxd/dx(sec(u) =(sec(u)tan(u)du/dxd/dx(csc(u) =(-csc(u)cot(u)du/dxdifferentiation rules cont. d/dx(sin-1(u) =(1/(1-u2)du/dxinverse trigonometric rulesd/dx(cos-1(u) = (-1/(1-u2)du/dxd/dx(tan-1(u) = (1/(1+u2)du/dxd/dx(cot-1(u) = (-1/(1+u2)du/dxd/dx(sec-1(u) = (1/(|u|u2-1)du/dxd/dx(

4、csc -1(u) =(-1/(|u|u2-1)du/dxintegration rules power rules:(undu) = (un+1)/(n+1) +c; only while n -1(u-1du) = ln(|u|) +cexponential rules:(udu) = u +c(budu) = bu/ln(b) - u +c, b1logarithmic rule:(ln(u)du) = uln(u) - u +c, u0integration rules cont. (sin(u)du) =-cos(u) + ctrigonometric rules(cos(u) du

5、) =sin(u) + c(tan(u) du) =-ln(|cos(u)|) + c(cot(u) du) =ln(|sin(u)|) + c(sec(u) du) =ln(|sec(u) + tan(u)|) + c(csc(u) du) =ln(|csc(u) + cot(u)|) + cintegration rules cont. trigonometric rules cont.(sec2(u) du) = tan(u) + c(csc2(u) du) = -cot(u) + c(sec(u)tan(u) du) = sec(u) + c(csc(u)cot(u) du) =-csc(u) + csummation formulasnnk