设函数f(x)=x*(x-1)*(x-2)...(x-99)(x-100),则f′(0)=
问题描述：
设函数f(x)=x*(x-1)*(x-2)...(x-99)(x-100),则f′(0)=
答
设（x-1)*(x-2)...(x-99)(x-100)为y,则有乘法求导公式有，f'(x)=y+x*y',所以f'(0)=y(0)=100!.
同理可求f'(1),f'(2),f'(3),......
答
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)...(0-9...