(3)y (4)y=2( )arcsin x) (5)y (6)y=2cos( tanx)lcos(tanx)I=-2cos(tanx) In 2 sir 1-Inx In x)= 6.求下列函数在指定点处的导数值 ( )f(o)=sin 3o (1-x) 解(1)r()=3c030+1-+2=3c083+1+,r(o)=4 (1-g2)2 (2)y 2x+ 5,y1=1=51-3e)3 (2) 22 2 y x xx x ′ ′ =− − − = − sin(4 3 )(4 3 ) 6 sin(4 3 ). (3) 2 2 (e ) e 1e 1e x x x x y ′ ′ = = + + . (4) 2 2arcsin 2(arcsin )(arcsin ) 1 x y xx x ′ ′ = = − . (5) 2 2 2 tan 2 tan 2 2 2 2 2 tan ln (tan ) ln sec ( ) 2ln sec x x x y a a x a a x x a x xa ′′ ′ = = =⋅ . (6) 3 3 3 33 y x x x xx ′′ ′ = =− 2cos(tan )[cos(tan )] 2cos(tan )sin(tan )(tan ) 3 2 = −3sin(2 tan ) tan (tan ) x x x ′ 22 3 = −3tan sec sin(2 tan ) x x x . (7) 2 2 1 1 sin sin 2 1 11 2 ln 2(sin ) 2 2ln 2sin (sin ) x x y x x x ′′ ′ = = 2 2 1 1 sin sin 2 1 1 1 ln 2 2 2 2ln 2sin cos ( ) 2 sin x x x xx x x = =− ′ . (8) 1 1 ln ln 2 22 1 1 1 1 ln (e ) e ( ln ) ( ln ) x x x x x x x y xx x x x x xx − ′′ ′ = = =− += . 6. 求下列函数在指定点处的导数值: (1) 2 ( ) sin 3 , 0 1 f ϕ ϕϕ ϕ ϕ = + = − ; (2) 1 3 arcsin 2 , 4 y xx x = = ; (3) 5 3e 5(1 ), 1 x y xx − = − − =− . 解 (1) 22 2 22 22 12 1 ( ) 3cos3 3cos3 , (0) 4 (1 ) (1 ) f f ϕϕ ϕ ϕϕ ϕ ϕ ϕ −+ + ′ ′ =+ =+ = − − . (2) 3 2 2 4 1 2 16 arcsin 2 , (3 3 π ) 9 1 4 x y xy x x x = ′ ′ =− + = − − . (3) 5 5 1 15e 5, 5(1 3e ) x x y y − =− ′ ′ =− + = −