7.求下列函数的导数 (1) y=Insec x+ tan x) (2) y=In tan+arctan(tan - (3) y=sin"xcosnx (4) arcsin. 7)y= x arcsin+√4-x ( 8) y=sh-ch3x (9) y=In chx chx (10)y=a4+x“+a 解(1)y secx tanx+ sec 1 sec x secx+ tan x Isec cscw+ (3)y=nsin"-lxcox cosnx-nsin"xsin nx= nsin"-lxcos(n+1)x (4)y 1-(1+x)-(1-x) (1+x)2 cosx2sin2x-sinx22sin xcos x 2xcosx sin x-2sinx2cosx (5)y sin x (7) y=arcsin+x arcsin (8)y=ch-(--)ch3x+ 3sh-sh3x=--3ch-ch3x+ 3sh-sh3x (9)y= shx -thx(l h2x (10) y=a Ina(a)+ax-+a In a(x)4 7. 求下列函数的导数: (1) ln(sec tan ) y xx = + ; (2) 1 ln tan arctan( tan ) 2 22 x x y = + ; (3) sin cos n y x nx = ; (4) 1 arcsin 1 x y x − = + ; (5) 2 2 sin sin x y x = ; (6) 2 1 1 y x x = + + ; (7) 2 arcsin 4 2 x yx x = +− ; (8) 2 y x sh ch3 x = ; (9) 2 1 ln ch 2ch y x x = + ; (10) xaa aax ya x a =++ . 解 (1) 2 sec tan sec sec sec tan xx x y x x x + ′ = = + . (2) 2 2 2 2 1 1 sec sec 2 24 2 1 csc 1 tan 1 tan 1 3cos 2 42 2 x x y x x x x ′ = + =+ + + . (3) 1 1 sin cos sin sin sin cos( 1) n nn y n xcox nx n x nx n x n x − − ′ = −= + . (4) 2 1 1 (1 ) (1 ) 1 1 1 (1 ) 2 (1 ) (1 ) 1 2 1 1 x x y x x xxx x x x − + −− ′ = =− −− + − + − + + . (5) 22 2 2 2 4 3 2 cos sin sin 2sin cos 2 cos sin 2sin cos sin sin x x x x xx xx x x x y x x − − ′ = = . (6) 22 2 2 2 12 1 (1 ) ( 1 ) 21 1 ( 1 ) x y x x x xx x ′ =− + =− ++ + + ++ . (7) 2 2 11 2 arcsin arcsin 22 2 2 4 1 4 x x x y x x x − ′ =+ + = − − . (8) 2 2 22 2 22 2 y xx xx ch ( )ch3 3sh sh3 ch ch3 3sh sh3 x x xx x x ′ = − + =− + . (9) 3 3 2 sh sh 1 2 th (1 ) th ch 2ch ch x x y xx x x x ′ =− = − = . (10) 1 ln ( ) ln ( ) x aa a x aa x a y a aa a x a ax − ′′ ′ = ++