一道求导的问题

一道求导的问题y=(x-1)(x-2)(x-3)...(x-10) (x>10)的导函数

热心网友

y=(x-1)(x-2)(x-3)......(x-10) (10)---lny=ln(x-1)+ln(x-2)+ln(x-3)+......+ln(x-10)---y'/y=1/(x-1)+1/(x-2)+1/(x-3)+......+1/(x-10)---y'=y[1/(x-1)+......+1/(x-10)]. 用此式作为结果是很好的.=(x-1)(x-2)......(x-10)[1/(x-1)+1/(x-2)+......+1/(x-10)].=(x-2)(x-3)......(x-10)+(x-1)(x-3)......(x-10)+(x-1)(x-2)(x-4)......(x-10)+......+(x-1)(x-2)......(x-9).用此式作结果过于冗长.