问题 解答题
(选做题)求下列函数的导数:
(1)y=(2x3-x+
1
x
)4
;                       
(2)y=
1
1-2x2

(3)y=sin2(2x+
π
3
)
;                        
(4)y=
1+x2
答案

(1)y=4(2x3-x+

1
x
)3(6x2-1-
1
x2
)

(2)y′= -

(
1-2x2
)
1-2x2
=-
1
2
 •
1
1-2x2
•(-4x)
1-2x2
=
2x
1-2x2
(1-2x2)2

(3)y=2sin(2x+

π
3
) cos(2x+
π
3
)•2 =2sin(4x+
3
)

(4)y=

1
2
(1+x2)-
1
2
•2x=
x
1+x2

名词解释
单项选择题