Question

设函数y=f(x)可导,且f(x)导数=1/x^2+1,则df(1/x)=?

Answer 1

令t=1/x

那么df(1/x)=f`(t)dt=f`(t)(-1/x^2)dx=[1/(1+1/x^2)]*(-1/x^2)dx=(-1/1+x^2)dx