Question

求过曲线y=x+lnx上点(1,1)处的切线方程和法线方程.

Answer 1

切线斜率k1法线斜率k2,对y求导,y'=1+1/x当x=1时,k1=y'|x=1=2,k2=-1/k1=-1/2,切线方程：y-1=2(x-1),即y=2x-1,法线方程：y-1=-1/2(x-1)即 x-2y+1=0.