问题标题:
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.24B.-24C.10D.-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
范贵生回答:
∵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
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