已知函数 f(x)在 (0,+infty ) 内可导, (x)gt 0, lim _(xarrow +infty )f(x)=1, 且满足 lim _(harrow 0)([ dfrac {f(x+hx))(f(x))] }^dfrac (1{n)}-|||-=(e)^dfrac (1{x)}, 求 f(x)所满足的方程.