Question

设x>0时,可导函数f(x)满足:f(x)+2f(1/x)=3/x求f'(x)(x>0)

Answer 1

f(x)+2f(1/x)=3/x (1)
将x换成1/x
f(1/x)+2f(x)=3x (2)
(1)-(2)*2
-3f(x)=3/x-6x
f(x)=2x-1/x
f'(x)=2+1/x²

Answer 2

f(y)+2f(1/y)=3/y (y>0)
f(1/x)+2f(x)=3x （令x=1/y的结果)
f(x)+2f(1/x)=3/x
解方程组得f(x)=2x-1/x
f'(x)=2+(1/x)^2 (x>0)