Question

f(x)=(x-1)(x-2)(x-3)求导

f(x)=(x-1)(x-2)(x-3)
怎么求导、有简单的方法么
能一下看出f'(x)是几次多项式么

Answer 1

y=(x-1)(x-2)(x-3)
两边同时取自然对数得：
lny=ln(x-1)+ln(x-2)+ln(x-3)
两边同时对x求导得：
y '/y=1/(x-1)+1/(x-2)+1/(x-3)
所以y '=y[1/(x-1)+1/(x-2)+1/(x-3)]
=(x-2)(x-3)+(x-1)(x-3)+(x-1)(x-2)