设f(x)=x(x-1)(x-2)...(x-100),f'（0）=我知道答案是100!,但是我想要详细的过程,

来源：学生作业学帮网编辑：学帮网时间：2024/05/27 01:35:53

设f(x)=x(x-1)(x-2)...(x-100),f'（0）=
我知道答案是100!,但是我想要详细的过程,

f ' (x)={x[(x-1)(x-2).(x-100)]}'
=x'*[(x-1)(x-2).(x-100)]+x*[(x-1)(x-2).(x-100)]'
=[(x-1)(x-2).(x-100)]+x*[(x-1)(x-2).(x-100)]'
f '(0)=[(x-1)(x-2).(x-100)]+0*[(x-1)(x-2).(x-100)]'
=[(0-1)(0-2).(0-100)]=100!(总共100数相乘为正)