Question

已经复合函数f(√x)=arctanx,则导数f(x)=?

Answer 1

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).