5 ú¨? ??ú¨±s ? p/ f ?￥ú¨? ? ò yx x x=+ ?+ 32 21, p ′′′y  ó yx x= 4 ln  p ′′y  ? y x x = + 2 1  p  ′′y ? y x x = ln 2  p ′′y  ? y= sin 3 x p a′′y ′′′y  × yx x= 3 cos  p a  ′′y ′′′y ? yx x = 23 e  p  ′′′y ù yx x = ? earcsin 2 ′′y p  ú yx x= 3 2cos  p  y ()80 ? yx x= +()s21 2 h p . y ()99 3  1 ,46'',143' 2 +=?+= xyxxy 6''' =y b  2  b 33 ln4' xxxy += 22222 7ln1234ln12" xxxxxxxy +=++=  3 2 2 3 2 1 21 43 21 ' 1 2(1 ) xxx x x x y x x +? + + == + +  31 2 22 2 53 2 3 (4 6 )(1 ) (4 3 )(1 ) 38 2 " 2(1 ) 4(1 ) xx xx x xx y x x ++?+ + 8+ + + + b  4 3 321 ln21 ln2' x x xxxxy ? =???= ???  4 431 5ln6 )ln21(32" x x xxxxy ? =???= ??? b  5  3223 cos3)3(cos' xxxxy =?= 3432323 sin9cos6)3)(sin(3cos6" xxxxxxxxxy ?=?+=  3323343 ''' 6cos 6 sin (3 ) 36 sin 9 cos (3 )yxxxxxxxx=? ?? ? ? 2 x 3 33 6 54 sin (27 6)cosx xx=? ? ? xb  6 xxxx x xxxxy sin 2 1 cos3) 2 1 )(sin(cos3' 2 5 232 ?=?+=  83 35 2 22 15 1 1 " 6 cos 3 ( sin ) sin (cos ) 42 yx xx x x xx x x x =+? ? ? 3 2 2 11 (6 )cos sin 44 x xxx=? ? x 13 2 22 133 1 1 ''' (6 )cos (6 )( sin ) sin cos 24 84 22 xx yxxxxxxx x x =? + ? ? ? ? 31 22 15 1 57 (6 )cos ( )sin 888 x xx x=? + ? xb  7  xxx exxxexxey 32323 )32()'3(2' +=+= xxx exxxexxexy 32323 )2129()'3()32()62('' ++=+++=  xxx exxxexxexy 32323 )185427()'3()2129()1218(''' ++=++++= b  8 222 ) 1 1 arcsin2()'(arcsinarcsin)'(' 2 2 xxx e x xxxexexy ??? ? +?=+?=  ; )1( )34( arcsin)12(2 )1( )2( ) 2 1 ( 1 2 arcsin2) 1 1 arcsin2)(2( )' 1 1 arcsin2() 1 1 arcsin2()'(" 2 22 22 2 3 2 2 2 2 3 2 22 22 2 x xx xx e x xx xx e x x x x xe x xxx e x xxe x xxxy ? ?? ?? ? ? ? ? ? ? ? ? ? ? ? ? +?= ? ? ? ? ? ? ? ? ? ? ? ? ?+ ? ??+ ? +??= ? +?+ ? +??=  9 (80) 3 (80) 1 2 (79) 2 (78) 3 (77) 80 80 80 cos 2 3 cos 2 6 cos 2 6cos 2y x xC x xC x xC x=+ + + 80 3 79 2 78 77 2 cos 2 80 2 3 sin 2 3160 2 6 cos 2 82160 2 6sin 2x xxx xx=+? ?? ??x 80 2 2 2 ( 4740)cos 2 (120 61620)sin 2x xxx??=? +? ?? x x b  10 (99) 2 (99) 1 (98) 2 (97) 99 99 (2 1)sh 4 sh 4shyx xCxxC=+ + + 2 (2 1)ch 99 4 sh 4851 4ch x xxx=+ +? +?x 2 (2 19405)ch 396 shx xx=+ + xb ? p/ f ?￥ ¨? ?  n ()n y 84 ò yx= sin 2 ω  ó yx x = 2ln ? y x x = e  ? y x x = ?+ 1 56 2  ? ye x x = α βcos  × yxx= +sin cos 44 . 3  1 ) 2 2cos(2)2cos1( 2 1 1)()( πωωω +?=?= ? n xxy nnnn 1 1 2sin(2 2 nn n x )ω ωπ ? ? =+b  2 () ( ) () 0 (2 ) (ln ) n nkxnkk x n k yC ? = = ∑ (1) 1 1 ln 2 2 ln 2 ln 2 k n nx kxk n k xC x ? ? = ?? =? + ? ?? ?? ∑ 1 1 (1) ( 1)! 2 ln 2 ln ln 2 kn xn knk n k k k xC x ? ? = ???? =?+ ? ?? ?? ∑ b  3 ∑∑ = + = ? ? = ? ? ? ? ? ? = n k k k xk n n k k knxk n n x k eC x eCy 0 1 0 )( )()( !)1(1 )( 1 0 !)1( + = ? = ∑ k kn k k n x x k Ce b  4?? 2 1 3 1 ? ? ? = xx y  () () () 11 32 nn n y xx ???? =? ???? ?? ???? 11 11 (1) ! (3) (2) n nn n xx ++ ? ? =? ? ? ? ?? ? ? 0 11 1 0 (2)(3) 1 (1) ! (1) ! (3)(2) (2) (3) n knk n k nn nk k xx xx x x ? = ++ ?+ = ?? =? =? ?? ? ? ∑ ∑ 1k+ b  5 [] )( 0 )()( )cos()( k n k knxk n n xeCy β α ∑ = ? = 0 cos( ) 2 n xknkk n k k eC x α π αβ β ? = =+ ∑ b  6 xxxxy 22222 cossin2)cos(sin ?+= 2 1 1sin 2 x=? 13 1(1cos4) 44 cos4x x=? ? = +  ?[ () 1 4 cos(4 ) 2 nn n yx π ? =+b à ù?f ? ? ? ? ? ? <? ≥ = 0, ,0, )( 2 2 xx xx xf 85 ￥ò¨? ?b 3 ? H  ?0>x xxf 2)(' = 0<x H xxf 2)(' ?= b? 2 00 () (0) () 0 (0) lim lim 0 xx fx f x f xx + ?→+ ?→+ ?? ? ? ′ == ?? = 2 00 () (0) () 0 (0) lim lim 0 xx fx f x f xx ? ?→? ?→? ?? ?? ? ′ == ?? = V? b ||2)(' xxf = ?N¤? 2, 0, ''( ) 2, 0, 0 x fx x x >? ? =? < ? ? = ? ?i b ? ^? H2>n () 0, 0, () 0 n x fx x ≠ ? = ? = ? ?i b 4 ! ?iQ V± p fx() ò [( )]fx 2 ′′′ ó 1 f x ′′′ ? ??? ??? ? ?? ? ?  ? [(ln)]fx′′ ? [ln ( )]fx′′ ? [( )]fe x? ′′′ × ])tan(arc[ ′′xf . 3  1  )('2)')((')]'([ 2222 xxfxxfxf == )('2)(''4)(')'2()')((''2')]'([ 2222222 xfxfxxfxxxxfxf +=+=  222222 2232 [ ( )]''' 4 '''( )( ) ' (4 ) ' ''( ) 2 ''( )( ) ' 8 '''( ) 12 ''( ) 2 f x xfxx x fx fxx xfx xfx=++=+b  2 ' 2 1111 ''ff f 1 x xx x x ′ ?? ?? ???? ?? ==? ?? ???? ???? ?? ???? ????  '' 2243 111111112 '' ' '' 'ff ff 1 f x xxxx xxxx ′′ ?? ?? ????? ? ?? ?? ?? =? ? = + ?? ????? ? ?? ?? ???? ?? ????? ? ?? ?? ???? x  6554 1 1 14 12 16 1 fffff x xxxxxxx ′′′ ?? ?? ?? ?? ?? ?? ′′′ ′′ ′′ ′=???? ?? ?? ?? ?? ???? ?? ?? ?? ?? ?? ?? x 86 2 6 11 1 1 66fxfxf x xx ?? ?? ?? ?? ′′′ ′′ ′=? + + ?? ?? ???? ?? ?? ?? ?? x b  3 () ( ) x xf xxfxf ln' )'(lnln')]'(ln[ == , () ( ) ( ) ( ) 22 ln'ln'')'(ln')'(lnln'' ')]'(ln[ x xfxf x xxfxxxf xf ? = ?? = b  4 )( )(' )]'([ln xf xf xf = , ( ) )( )(')()('' ')]'([ln 2 2 xf xfxfxf xf ? = b  5 )(')')((')]'([ xxxxx efeeefef ????? ?== 2 [ ( )]'' ''( )( ) ' ( ) ' '( ) ''( ) '( ) xxxxxxxxxx f e efe e e fe e fe efe ????????? =? ? = + ? x , 22 [ ( )]''' '''( )( ) ' ( ) ' ''( ) ''( )( ) ' ( ) ' '( ) xxxxxxxxxx f eefeeefeefeeefe ????? ????? =+++ ? x 32 '''( ) 3 ''( ) '( ) xx xxx efe efe efe ?????? =? ? ? b  6 2 '(arctan ) [ (arctan )]' '(arctan )(arctan ) ' 1 f x fxf xx x == + , 22 22 (1 ) ''(arctan )(arctan ) ' (1 )' '(arctan ) [ (arctan )]'' (1 ) x fxxxf fx x +? = + x 22 ''(arctan ) 2 '(arctan ) (1 ) f xxf x x ? = + b 5 ?¨ Leibniz T9 ?  () (0) n y ò xy tanarc=  ó yx= arcsin b 3  1? 222 )1( 2 '', 1 1 ' x x y x y + ?= + =  7 0x =  V ¤ 0)0('',1)0(' == yy b ? T H p ¨? ? ¤? 1)1(' 2 =+ xy x n 1n> ∑ = +? =+ n k kknk n xyC 0 )(2)1( 0)1(  ?i?   Te?1 0'')'1( 2 =+ x 87 (1) 2 () (1) (1) (1 ) 2 2 0 2 nn n nn yxnyx y +? ? ++ ?+ ?= [ } ?¤??w T 0=x )0()1()0( )1()1( ?+ ??= nn ynny  V7¤? 1 2 () (1) ( 1)!, ; (0) 0, n n nn y n ? ? ? ?? = ? ? ? 1  ? 1 } ?b  2? 13 3 2222 2 1' '(1 ),''( )(1 )(1 )' (1 ) 21 xy yxy x xxx x ?? ? =? =? ? ? = ? = ?  7  0=x V¤  O b ? T H p ¨? ? ¤? 0)0('',1)0(' == yy '')1(' 2 yxxy ?= '')1(' 2 yxxy ?= x n 1n≥ ∑∑ = +? = +? ?= n k kknk n n k kknk n xyCxyC 0 )(2)2( 0 )()1( )1()(  ' )()1()(2)2()()1( )1(2)1( nnknnn ynnxnyxynyxy ????=+ +++ (1) () (2) 2 (1) () (1 ) 2 ( 1) nnn n n xynyy xxnyny ++ + += ?? ?? [ } ?¤??w T 0=x )0()0( )(2)2( nn yny = +  V7¤? 2 () [( 2)!!] (0) 0 n nn y n ? ? = ? ?  1  ?   1 } ?b 6 / ?f ? p 2 2 dy dx  ò exy xy 2 2 0 + ?=; ó 0)tan( =?+ xyyx ; ? 20yxxysin ln+=; ? 33 30xy axy+ ?=. 3  1? T H p?μ x 88 0'2)'2()'()'( 222 22 =??+=?+ ++ yxxyyxeyxyxe yxyx   p?¤? x )' = 22 ( )'(2') (2')'(2 xy xy exyxye xy xyxy ++ +++ +?+ 22 22 (2 ') (2 '') 2 4 ' '' 0 xy xy exye yyxyxy=+++??? V73 2 22 2 2 ])'('442[2'4 '' xe yxyxeyxy y yx yx ? +++?+ = + +  ? 2 2 2 )(2 ' xe eyx y yx yx ? ? = + + b  2? T H p?μ x x 0')'1)((sec)'()')((sec 22 =??++=?++ xyyyyxxyyxyx   p?¤? 22 2sec ( ) tan( )( )'(1 ') sec ( )(1 ')' ' ( ')'x yxyxyy xyyyxy+++++++?? 2 2sec()tan()(1')sec()'2''xy xy y xyy yxy=+++++??0= V73 )(sec '2)'1)(tan()sec(2 '' 2 2 yxx yyyxyx y +? ?+++ =  ? )(sec )(sec ' 2 2 yxx yyx y +? ?+ = b  3? T H p?μ x 0'lncos2sin'2 =?+++ y y x yxyxy   p?¤? x 0'')'( ' 2sin2cos'4sin''2 2 2 =?+??+?+ y y x y y x y y xyxyxy  89 V73 xyxy yxyyxyyxy y sin2 )'('2cos'4sin2 '' 2 223 + +?? =  ? xyx yyxy y sin2 lncos2 ' 2 + + ?= b  4? T H p?μ x x 0'33'33 22 =??+ axyayyyx   p?¤? 0''3'6''3)'(66 22 =??++ axyayyyyyx  V73 2 2 '2)'(22 '' yax ayyyx y ? ?+ =  ? axy xay y ? ? = 2 2 ' b 7 / ? ?? T￥f ? p dy dx 2 2  ò xat ybt = = ? ? ? 2 3 , , ó xat t yat t = = ? ? ? cos , sin , ? xt t yt t =? = ? ? ? (sin) cos , 1 , ? xa yb t t = = ? ? ? ? e, e, ? xt yt =+ =? ? ? ? 1 1 , , × ? ? ? = = .cos ,sin bty atx 3  1 ta b at abtatbt at atbtatbt dx yd 23 2 32 2323 2 2 4 3 )2( )2)(3()2)(6( ])'[( ')'()'()'(')'( = ? = ? = b  2 2 23 ( sin ) ''( cos ) ' ( sin ) '( cos ) '' [( cos )'] dy at t at t at t at t dx at t ? = 90 33 222 2 33 (2cossin)(cossin)(sincos)(2sincos (cos sin ) ( 2)(sin cos ) 2 (cos sin ) (cos sin ) a t at t a t at t a t at t a t at t attt tttt a ttt a ttt )? ?++ + = ? ++ + == ?? b  3 2 23 ( cos ) ''[( (1 sin )]' ( cos ) '[ (1 sin )]'' [(1 sin )]' dytttttttt dx t t ?? ? = ? 3 2 3 ( 2sin cos )(1 sin cos ) (cos sin )( 2cos sin ) (1 sin cos ) 22sin cos (1 sin cos ) tt t tt t tt t tt t tt t tttt tt t ?? ?? ?? ?+ = ?? +? ? = ?? b  4 2 23 ( ) ''( ) ' ( ) '( ) '' [( ) '] tt tt t d y be ae be ae dx ae ?? ? ? = 3 23 2 2 tt tt t t be e be e b e ae a ?? ? ?? == ? b  5 2 2 3 ( 1 ) ''( 1 ) ' ( 1 ) '( 1 ) '' [( 1 ) '] dy t t t t dx t ?+??+ = + 3 3 2 33 11 (2 1 ) 2(1 ) 4( 1 ) (2 1 ) 2( 1 )[4( 1 ) ] tt tt tt ??? ? =? += ?? ?+ ?+ ?? ?b  6 2 2'3 (cos ) ''(sin ) ' (cos ) '(sin ) '' (sin ) d y bt at bt at dx at ? = 23 (sinsin coscos) cos b a at bt b at bt aat ?? = 23 (sin sin cos cos ) cos b a at bt b at bt aat + =? b 8 ?¨Qf ?￥ p? T dx dy y = ′ 1 ￡ ü ò 32 2 )'( '' y y dy xd ?= ; ó dx dy yy y 3 3 2 5 3 = ′′ ? ′ ′′′ ′ () () . ￡  1 2 2 1 () () ' dx d dx d dy dy dy dy y == 22 2 1' 1' '1 ' (') (') (') ' (') dy dy dx y y y dy y dx dy y y y =? =? =? ? =? b 3  2 () 32 332 '' () [ ] ' dx d dx d y dy dy dy dy y ==? 34 1'' ' 3 (') (') dy y dy ydy ydy =? + ' 22 34 34 1 '' '' ' ''' 1 3( '') 1 3( '') ' ''' 3 (') (') (') ' (') ' (') dy dx y dy dx y y y y y ydxdy ydxdy y y y y y ? =? + =? ? + ? = b 5 91 9 p/ f ?￥ú¨±s ò ,tan 3 xxy ?= p  dy 2 ó yx x = ?4 e  p  dy 4 ? y x x = +1 2  p  dy 2 ? y x x = ? sec 2 1  p  dy 2 ? yx x= sin 3  p  dy 3 × yx x =  p  dy 2 ? y x x = ln  p d  y n ù yx x n = cos 2  p . dy n 3  1 2 2 3 1 (tan)(1sec) 3 dy x x x dx ? =? ? 2 2 3 1 (tan)tan 3 x xx ? =? ? dx 52 222 33 21 [ ( tan ) (1 sec ) ( tan ) (2 tan sec )] 93 dy x x x x x x xdx ?? =? ? ? ? ? 2 42 2 5 3 2 tan 6sec tan ( tan ) 9(tan ) xxxx dx xx +? = ? b  2 4 44()(4)4 4 0 [()() ] kkxk k dy C x e dx ?? = = ∑ 4 44 4 0 4! (1) (4 )! kkk k Cx e k ??? = =? ? ∑ 4x d 4234 )24967216( dxexxxx x? +?+?= b  3 dx xx dx x xxx x dy 22 2 2 2 1 1 11)2( 12 1 + ?= ?+??? + =  2 22 33 32 22 32 22 22 [] 1 2(1 ) (1 ) xx d y dx dx xx xx xx + =+ = + ++ b  4 2 13 3 22 2 tan sec 1 sec (2 ) sec [( 1) tan ] [] 2 (1) (1) (1) xx xx xx xx dy dx dx ?? =?? = ?? ? ?  2 3 2 2 sec tan [( 1) tan ] sec [2 tan ( 1)sec 1] (1) xxx xx xxxx x dy x ? ??+ +? ?? = ? ? ? ? 2 2 5 2 2 3sec[( 1)tan ](2) 2 (1) xx x x x dx x ? ???? ?? ? ? ? ? 92 22 2 2 2 2 5 2 2 sec [( 1) (1 2 tan ) 2 ( 1) tan 2 1] (1) xx x xx x x dx x ?+ ? ? ++ = ? b  5 333 27(sin 3 cos3 )[ (sin 3 ) ''' 3 '(sin 3 ) '']dy x x x x dx=+ x xxd=? + xb  6  dxxxdxxededy xxxxx )ln1()ln1( lnln +=+== 2 22 1 [( )'(1ln) (1ln)'] [(1ln) ] xx x d y x x x x dx x x dx x =+++ =++b  7 n n k knkk n n dx x xCyd ∑ = ? = 0 )()( ) 1 ()(ln 1 1 1 1 (1) ! ! ( 1)! ( )! [ln (1) (1) ] !( )! n n knk nk k nnknk n x dx xknkxx ?? + ?+ = ?? =+ ?? ? ∑ 1 1 (1) ! 1 ln n n n n k n x dx xk + = ? ?? =? ?? ?? ∑ b  8 n n k kknnk n n dxxxCyd ∑ = ? = 0 )()( )2(cos)( 0 !! ()[2cos(2 )] !( )! ! 2 n kk k nn k n x xd knk k π = =+ ? ∑ x 2 2 0 2cos(2 ) 2 (!) (!)( )! kk n n k k xx nd knk x π = + = ? ∑ b 10 p  ? 2 () x de ò x ^1M  ; ó )(tx ?= ^?WM  . 3  1  dxedxeed xxx == )'()( 222 )'()()( dxedxedxeded xxxx === b  2  dttedxedxeed txxx )(')'()( )( ? ? === 2() ()2 () ( '())[ '()]' xt t de de tdt e t dt ?? == { } () 2 2 [ '( )] ''( ) t ett ? ??=+dtb 11 !  ?iQ V± O b fu() gu() gu()> 0 ò? xu tan= H p d  f 2 ó? u= vav x= ln H p  dg 2 93 ? dfugu 2 [()()] ? dgu 2 [ln ( )] ? ? ? ? ? ? ? )( )( 2 ug uf d  3  1  xdxxfdxxuufdf 2 sec)(tan')(')(' == 222 ''( )[ '( )] '( ) ''( )d f f u u x dx f u u x dx=+ 2 2 42 [ "(tan )sec 2 '(tan )sec tan ]f xxfxxxd=+ xb  2 xvu ln==  11 1 '( ) '( ln ) 2ln 2 ln dg du dv dg dx g u dx g x dx du dv dx x x xx == =  22 2 "( ) '( )(2 ln ) ' [] 2ln (2ln) du dv gu gu x x dv dx dg dx xx xx =? 2 22 11 '( )[2 ln 2 ( )] "( ) 2ln (2 ln ) (2 ln ) gu x x gu x x dx xx xx ?? +? ?? =? ?? ?? 2 3 2 2 "(ln)ln '(ln)(12ln) 4ln gxxgx x dx xx ?+ = b  3 duugufugufugufd )](')()()('[)]()([ +=  222 )]'()()()('[)](')()()('[)]()([ duugufugufudugufugufugufd +++= 22 [ '()() () '()] [ "()() 2 '() '() () "()]f ugu fug u du f ugu f ug u fug u du=+ ++ + b  4 du ug ug ugd )( )(' )]([ln =  2 2222 2 '() '() '() "()() ( '()) [ln ( )] [ ]' () () () () gu gu gu g ugu gu dgu du du du du gu gu gu g u ? =+ =+ b  5 du ug ugufuguf ug uf d )( )(')()()(' )( )( 2 ? = ? ? ? ? ? ?  94 2 2 2 2 2 )( )(')()()(' )( )(')()()(' )( )( du ug ugufuguf ud ug ugufuguf ug uf d ′ ? ? ? ? ? ? ? + ? = ? ? ? ? ? ? 2 2 '( ) ( ) ( ) '( ) () fugu fugu du gu ? =+ 2 2 2 3 "() () ()() "() 2 '() '()() 2 ()( '()) () f ug u fugug u f ug ugu fu g u du gu ?? + b 12. ?¨ ?DB ,E￡ ü x n n n x n e x ex 1 1 )( 1 1 )1( + ? ? = ? ? ? ? ? ? ? ? b ￡ ? H1=n xxx n x n e xx eeex 1 2 11 )( 1 1 1 )' 1 ()'()( ? === ?   5? ?b L ! H 5?? ?b5? H kn ≤ 1+= kn () () 11 11 1() 1 1 ()()' ()' kk nn k k k xx xx xe xe kxe xe x ?? ??? ? ==+ ??? ? ??? ? () 11 11 12(1) 1 (1) (1) () k kk kkk xx x kx e x e k e e xx ? ??? + x ′ ′ ??? ? ? ?? =? =? ??? ? ? ??? ? ? ? ? ? 11111 2 (1) (1) (1) 1 (1) () kkk xxx k keke e xxx x ?+ ++ + ?? ??? ? =? +?= ?? ?? 1 2 x e 59? ?b? ?DB ,E V?' 5 ?μ?? ??? ?b 95