f(x)=x(x-1)(x+2)(x-3)(x+4)……(x+100),求f'(1)

来源：学生作业帮编辑：搜搜考试网作业帮分类：数学作业时间：2024/06/22 21:04:19

f'(x)=[x'(x-1)(x+2)(x-3)(x+4).(x+100)]+[x(x-1)'(x+2)(x-3)(x+4).(x+100)]+...+[x(x-1)(x+2)(x-3)(x+4).(x+100)']
除开第2项外,其他各项均含有因式(x-1),当x=1时,这些项均为0
故
f'(1)=x(x-1)'(x+2)(x-3)(x+4).(x+100)|x=1
=1*3*(-2)*5*(-4)*...*(-98)*101
=-101!/100

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