Differential Equations with Boundary Value Problems- Zill & Cullen {7th Edition}.pdf

Rules 1 . Constant : d dx c = 0 2 . Constant Mu ltiple : d dx cf ( x ) = c ? f ( x ) . Sum : d dx [ f ( x ) ± g ( x )] = ? f ( x ) ± ? g ( x ) 4 . Product : d dx f ( x ) g ( x ) = f ( x ) ? g ( x ) + g ( x ) ? f ( x ) 5 . Quotient : d dx f ( x ) g ( x ) = g ( x ) f ( x ) ? f ( x ) g ( x ) [ g ( x )] 2 6 . Chain : d dx f ( g ( x )) = ? f ( g ( x )) ? g ( x ) 7 . Power : d dx x n = nx n ? 1 8 . Power : d dx [ g ( x )] n = n [ g ( x )] n 1 ? g ( x ) Functions Trigonometric : 9 . d dx sin x =cos x 10 . d dx cos x = ?sin x 11 . d dx tan x =sec 2 x 12 . d dx cot x = ?csc 2 x 13 . d dx sec x =sec x tan x 14 . d dx csc x = ?csc xcot x Inverse trigonometric : 15 . d dx sin ? 1 x = 1 1 ? x 2 16 . d dx cos ? 1 x = ? 1 1 ? x 2 17 . d dx tan ? 1 x = 1 1 + x 2 18 . d dx cot ? 1 x = ? 1 1 + x 2 19 . d dx sec ? 1 x = 1 x x 2 ? 1 20 . d dx csc ? 1 x = ? 1 x x 2 ? 1 Hyperbolic : 21 . d dx sinh x =cosh x 22 . d dx cosh x =sinh x 23 . d dx tanh x =sech 2 x 24 . d dx coth x = ?csch 2 x 25 . d dx sech x = ?sech xtanh x 26 . d dx csch x = ?csch xcoth x Inverse hyperbolic : 27 . d dx sinh ? 1 x = 1 x 2 + 1 28 . d dx cosh ? 1 x = 1 x 2 ? 1 29 . d dx tanh ? 1 x = 1 1 ? x 2 30 . d dx coth ? 1 x = 1 1 ? x 2 31 . d dx sech ? 1 x = ? 1 x 1 ? x 2 32 . d dx csch ? 1 x = ? 1 x x 2 + 1 Exponential : 33 . d dx e x = e x 34 . d dx b x = b x(ln b ) Logarithmic : 35 . d dx ln x = 1 x 36 . d dx log b x = 1 x(ln b ) ??? 3 REVIEW OF DIFFERENTIATIONBRIEF TABLE OF INTEGRALS 1 . 1 ,1 1 n n u udu Cn n ??????? 2 . 1 ln du u C u ??? 3 . uu edu e C ??? 4 . 1 ln uu adu a C a ??? 5 . sin cosudu u C ?? ?? 6 . cos sin udu u C ??? 7 . 2 sec tan udu u C ??? 8 . 2 csc cot udu u C ?? ?? 9 . sec tan secuudu uC ??? 10 . csc cot cscuudu uC ?? ?? 11 . tan ln cosudu u C ?? ?? 12 . cot ln sinudu u C ??? 13 . sec ln sec tanudu u u C???? 14 . csc ln csc cotudu u u C???? 15 . sin sin cos uuduuuuC ???? 16 . cos cos sin uuduuuuC ???? 17 . 2 11 2