设函数f(x-1/x)=lnx,求f(x)的导数.

f(x-1/x)=lnx
令u=x-1/x
ux=x²-1
x²-ux-1=0,Δ=u²-4*(-1)=u²+4
x=[-(-u)±√(u²+4)]/2
=1/2*[u²±√(u²+4)]
=1/2*[u²+√(u²+4)]>0或1/2*[u²+√(u²+4)]