隐函数求导x^2+y^2-2x-6y+5=0求dy/dx和d^2y/dx^2当x=3,y=2

问题描述:

隐函数求导x^2+y^2-2x-6y+5=0
求dy/dx和d^2y/dx^2当x=3,y=2

x^2+y^2-2x-6y+5=0 对x求导:2x+2yy'-2-6y'=0 y'=(2x-2)/(6-2y) y'(3)=(6-2)/(6-4)=2.2x+2yy'-2-6y'=0 对x求导:2+2(y'y'+yy'')-6y''=0 y''=(2+2y'^2)/(6-2y) y''(3)=(2+2*4)/(6-4)=5.