设y=f[(3x-2)/(3x+2)]且f'(x)=arctanx^2,则dy/dx|x=0的值多少

问题描述:

设y=f[(3x-2)/(3x+2)]且f'(x)=arctanx^2,则dy/dx|x=0的值多少
为什么我把[(3x-2)/(3x+2)]直接带入arctanx^2里
就是arctan[(3x-2)/(3x+2)]^2|x=0
算出来的结果不一样?

dy/dx|x=0 =df[(3x-2)/(3x+2)]/dx|x=0 =arctan[(3x-2)/(3x+2)]^2*[(3x-2)/(3x+2)]'|x=0
=3π/4