Question

1道数学高数隐函数题 说明理由 1.设函数y=y(x) 由x^2+5xy+y^2-2x+y-6=0确定 求y' 和y''

Answer 1

两边对x求导：2x+5y+5xy'+2yy'-2+y'=0

得：y'=(2-2x-5y)/(5x+2y+1)

代入x=1,y=1,得：y'=-5/8

将y'再对x求导,得：y"=[(-2-5y')(5x+2y+1)-(2-2x-5y)(5+2y')]/(5x+2y+1)^2

将x=1,y=1,y'=-5/8代入得：y"=[(-2+25/8)8+5(5-5/4)]/8^2=111/256