y=f(x)=lnx+1/ex
f'(x)=1/x-1/ex²
点(1,f(1))处切线的斜率=f'(1)=1-1/e
∴切线方程为y-f(1)=(1-1/e)(x-1)
即:(1/e-1)x+y+1-2/e=0