A.(π/3 "," √3/2)

B.("-" π/3 ",-" √3/2)或(π/3 "," √3/2)

C.(2kπ+π/3 "," √3/2)(k∈Z)

D.(2kπ+π/3 "," √3/2)(k∈Z)或(2kπ"-" π/3 ",-" √3/2)(k∈Z)

解析:y'=cos x,y'"|" _(x=x_0 )=cos x0=1/2,则x0=2kπ+π/3(k∈Z),y0=√3/2 或x0=2kπ-π/3(k∈Z),y0=-√3/2.

答案:D

6.已知f(x)=x2+ex,则f'(0)=　　　　　;[f(1)]'=　　　　　.

解析:∵f'(x)=2x+ex,∴f'(0)=1.

　　∵f(1)=1+e,∴[f(1)]'=0.

答案:1　0

7.已知f(x)=cos x,g(x)=x,则关于x的不等式f'(x)+g'(x)≤0的解集为　　　　　　　　　　.

答案:{x├|x=π/2+2kπ"," k"∈" Z┤}

8.在曲线y=4/x^2 上求一点P,使得曲线在该点处的切线的倾斜角为135°,则点P坐标为　.

解析:设点P(x0,y0),∵y'=(4/x^2 )'=(4x-2)'=-8x-3,

　　∴tan 135°=-1=-8x_0^("-" 3),∴x0=2.∴y0=1.

答案:(2,1)

9.曲线y=ln x在点M(e,1)处的切线的斜率为　　　　　,切线的方程为　.

解析:∵y'=(ln x)'=1/x,∴y'|x=e=1/e.∴曲线y=ln x在点M(e,1)处的切线的斜率为k=1/e.

　　∴切线方程为y-1=1/e(x-e),即x-ey=0.

答案:1/e　x-ey=0

10.求下列函数的导数:

(1)y=sin x-x+1;

(2)y=-2ex·x3;

(3)y=lnx/(x+1)-2x.