已知f′(x)=1/x，y=f[(x+1)/(x-1)]，求dy/dx．

已知f′(x)=1/x，y=f[(x+1)/(x-1)]，求dy/dx．
【正确答案】：y′=f′[(x+1)/(x-1)]•[(x-1)-(x+1)]/(x-1)²=[-2/(x-1)²]f′[(x+1)/(x-1)]， 又因为f′(x)=1/x，所以f′(x+1)/(x-)=(x-1)/(x+1)，故 dy/dx=-2/(x-1)²•(x-1)/(x+1)=-2/(x²-1)