Question

设Y是方程sin(xy)-1/y-x=1所确定的函数,求（1）y|x=o (2) y'|x=o

Answer 1

1）y|x=o

当x=0时

sin(0)-1/y-0=1

得：y|x=0 =-1

(2) y'|x=o

sin(xy)-1/y-x=1

两边对x求导：

cos(xy)(y+xy')+y'/y^2 - 1=0

当x=0时y=-1,

代入得：cos(0)(-1+0)+y'-1=0

得：y=-1

y'|x=0 =2