已经复合函数f(√x)=arctanx,则导数f(x)=?

令√x=t,则x=t^2,
f(√x)=arctan(x),
变量替换
f(t)=arctan(t^2)
对t求导,
f'(t)=[1/(1+(t^2)^2)]*(t^2)'
=[1/(1+(t^2)^2)]*(2t)
=2t/(1+t^4),
令t=x,
则f'(x)=2x/(1+x^4).