Question

设f(x)=x(x-1)(x-2)...(x-99)(x-100),则f'(0)等于（）。

A、-100
B、0
C、100
D、100！

Answer 1

【答案】：D
解析：因为f(x)=x*(x-1)*(x-2)...(x-99)(x-100)
所以f(0)=0
所以f′(0)=lim(x→0)[f(x)-f(0)]/(x-0)
=lim(x→0)f(x)/x
=lim(x→0)[x*(x-1)*(x-2)...(x-99)(x-100)]/x
=lim(x→0)(x-1)*(x-2)...(x-99)(x-100)
=(0-1)*(0-2)...(0-99)(0-100)
=100!