X(X-1)(X-2).(X-n)求导.

来源：学生作业学帮网编辑：学帮网时间：2024/05/04 17:14:21

设y=x(x-1)(x-2).(x-n)
lny=ln[x(x-1)(x-2).(x-n)]
lny=lnx+ln(x-1)+ln(x-2)+.+ln(x-n)两边求导
y'/y=1/x+1/(x-1)+1/(x-2)+.+1/(x-n)
y'=y*[1/x+1/(x-1)+1/(x-2)+.+1/(x-n)]
=(x-1)(x-2)...(x-n)
+x(x-2)...(x-n)
+x(x-1)(x-3)...(x-n)
+...
+x(x-1)(x-2).(x-n+1)

(X-1)(X-2).....(X-n)+
X(X-2).....(X-n)+
X(X-1)(X-3).....(X-n)+
...
X(X-1)(X-2).....(X-n+1)

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