f(x)的导数公式怎么推导？

Question

如题所述

Answer 1

f(x)=x(x-1)(x-2)(x-3)(x-4)(x-5)
lnf(x) = ln|x|+ln|x-1|+ln|x-2|+ln|x-3|+ln|x-4|+ln|x-5|
f'(x)/f(x) = 1/x + 1/(x-1) + 1/(x-2) + 1/(x-3) + 1/(x-4) + 1/(x-5)
f'(x) = f(x)[1/x + 1/(x-1) + 1/(x-2) + 1/(x-3) + 1/(x-4) + 1/(x-5)]
= x(x-1)(x-2)(x-3)(x-4)(x-5)[1/x+1/(x-1)+1/(x-2)+1/(x-3)+1/(x-4)+1/(x-5)]