若函数f(x)=(x-1)(x-2)(x-3)(x-4)(x-5),且f′(x)是函数f(x)的导函数,则f′(1)=( ) A.24 B.-24 C.10 D.-10
问题描述:
若函数f(x)=(x-1)(x-2)(x-3)(x-4)(x-5),且f′(x)是函数f(x)的导函数,则f′(1)=( )
A. 24
B. -24
C. 10
D. -10
答
∵f(x)=(x-1)(x-2)(x-3)(x-4)(x-5),
∴f′(x)=(x-1)′•(x-2)(x-3)(x-4)(x-5)+(x-1)•[(x-2)(x-3)(x-4)(x-5)]′
∴则f′(1)=(1-2)(1-3)(1-4)(1-5)=24.
故选A