4.2　导数的乘法与除法法则

1.已知f(x)=x-5+3sin x,则f'(x)=(　　)

A.-5x-6-3cos x B.x-6+3cos x

C.-5x-6+3cos x D.x-6-3cos x

答案:C

2.函数y=(x+3)2(x-1)在x=-1处的导数等于(　　)

A.-1 B.-2 C.-3 D.-4 学 ]

解析:∵y=(x+3)2(x-1)=x3+5x2+3x-9,

　　∴y'=3x2+10x+3. 学 ]

　　∴当x=-1时,y'=-4.

答案:D

3.若y=(1"-" x^2)/sinx,则y'=(　　)

A.("-" 2xsinx"-(" 1"-" x^2 ")" cosx)/(sin^2 x)

B.("-" 2xsinx+"(" 1"-" x^2 ")" cosx)/(sin^2 x)

C.("-" 2xsinx+"(" 1"-" x^2 ")" )/sinx

D.("-" 2xsinx"-(" 1"-" x^2 ")" )/sinx

解析:∵y=(1"-" x^2)/sinx,∴y'=("(" 1"-" x^2 ")'" sinx"-(" 1"-" x^2 ")(" sinx")'" )/(sin^2 x)=("-" 2xsinx"-(" 1"-" x^2 ")" cosx)/(sin^2 x).

答案:A

4.若f(x)=x2-2x-4ln x,则f'(x)>0的解集为(　　) . ]

A.(0,+∞) B.(-1,0)∪(2,+∞)

C.(2,+∞) D.(-1,0)

解析:函数f(x)的定义域为(0,+∞).由f'(x)=2x-2-4/x=(2"(" x"-" 2")(" x+1")" )/x>0.因为x>0,所以x>2.故f'(x)>0的解集为(2,+∞).

答案:C

5.曲线y=f(x)=2x-x3在点(-1,-1)处的切线方程为0(　　)

A.x+y+2=0 B.x+y-2=0 | Z|X|X|K]

C.x-y+2=0 D.x-y-2=0

解析:∵f(x)=2x-x3,

　　∴f'(x)=2-3x2,f'(-1)=2-3=-1.

故f(x)在点(-1,-1)处的切线方程为y+1=-(x+1),