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,
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![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,](/uploads/image/z/14295243-3-3.jpg?t=%E8%AE%BEf%28x%29%3Dx%28x-1%29%28x-2%29...%28x-100%29%2Cf%27%EF%BC%880%EF%BC%89%3D%E6%88%91%E7%9F%A5%E9%81%93%E7%AD%94%E6%A1%88%E6%98%AF100%21%2C%E4%BD%86%E6%98%AF%E6%88%91%E6%83%B3%E8%A6%81%E8%AF%A6%E7%BB%86%E7%9A%84%E8%BF%87%E7%A8%8B%2C)
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,
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,
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)