若方程cos(xy)-x^2·y=1 确定y是x的函数,求y''|(1,0)
问题描述：
若方程cos(xy)-x^2·y=1 确定y是x的函数,求y''|(1,0)
答
cos(xy)-x^2·y=1 两边对x求导
-sin(xy)*(y+xy')-2xy-x^2y'=0===>x=1,y=0,y'=0
-cos(xy)(y+xy')^2-(y'+y'+xy")-2y-2xy'-2xy'-x^2y"=0
===>x=1,y=0,y'=0,y"=0