f(x)=(x-1)(x-2)…(x-100),求fˊ(99)

当x不等于1，2，3，...,97,98,100时
f'(x)=f(x)/(x-1)+f(x)/(x-2)+...+f(x)/(x-100)+(x-1)(x-2)...(x-97)(x-98)(x-100)
因为f(99)=0
所以f'(99)=(99-1)(99-2)...(99-97)(99-98)(99-100)
=-98!

f'(x)=(x-1)(x-2)...(x-98)(x-100)
f'(99)=98*97*...*1*(-1)
=-98!

f'(x)=(x-2)…(x-100)+(x-1)(x-3)…(x-100)+…+(x-1)…(x-98)(x-100)+(x-1)…(x-99)

x=99时,除(x-1)…(x-98)(x-100)这项外,其他各项均含有(x-98),所以
f'(99)=98*97*…1*(-1)=-98!

f'=(x-2)(x-3)...(x-99)(x-100)+(x-1)(x-3)...(x-99)(x-100)+...+(x-1)(x-2)...(x-98)(x-100)+(x-1)(x-2)...(x-99)
f'(99)=(99-1)(99-2)...(99-98)(99-100)=-98!

=98*97*....*0*(-1)
=0