Question

已知：f（x）=(x-1)(x-2)(x-3)……（x-100)求f'(1)

过程说明一下，谢谢 ！结果好像是-1*2*3*4*5.......*99

Answer 1

解：可设函数g(x)=(x-2)(x-3)...(x-100),则g(1)=(-1)*(-2)*(-3)...(-99)=-99!.又函数f(x)=(x-1)g(x).求导得f'(x)=g(x)+(x-1)g'(x).∴f'(1)=g(1)=-99!.

Answer 2

看成f(x)=(x-1){(x-2)…(x-99)(x-100)}，f'(x)=[(x-1)*g(x)]'

Answer 3

5