Question

求函数y=(x-1)(x-2).(x-100)(x＞100)的导数

Answer 1

就是两边先取对数,对数求导法

两边取自然对数

lny＝ln(x－1)＋ln(x－2)＋…＋ln(x－100)

两边对x取导数

y'/y=1/(x-1)+1/(x-2)+...+1/(x-100)

y'=[1/(x-1)+1/(x-2)+...+1/(x-100)]y

=[1/(x-1)+1/(x-2)+...+1/(x-100)]*(x-1)(x-2).(x-100)