函数f(x)=(x+3)./(x^2+3)在x=3处的导数值是
问题描述：
函数f(x)=(x+3)./(x^2+3)在x=3处的导数值是
答
(u/v)'=(u'v-uv')/v^2
所以f'(x)=[(x+3)'(x^2+3)-(x+3)(x^2+3)']/(x^2+3)^2
=[(x^2+3)-(x+3)*2x]/(x^2+3)^2
=(-x^2-6x+3)/(x^2+3)^2
f'(3)=(-9-18+3)/(9+3)^2=-1/6