Question

求方程确定的隐函数的导数dy/dx，d2y/dx2

Answer 1

两边对x求导 dy/dx=0+d(xe^y)/dx dy/dx=e^y*dx/dx+x*e^ydy/dx dy/dx=e^y+x*e^ydy/dx dy/dx-x*e^ydy/dx=e^y dy/dx=e^y/(1-x*e^y) 很高兴为您解答，祝学习进步！ 有不明白的可以追问！ 如果您认可我的回答，请点击下面的【选为满意回答】按钮，谢谢

Answer 2

两边分别对x求导有： 2x+2yy'-(y+xy')=1 2x+2yy'-y-xy'=1 (2y-x)y'=y-2x+1 dy/dx=y'=(y-2x+1)/(2y-x)

Answer 3

两边对x求导
dy/dx=e^(x+y)*(1+dy/dx)
[1-e^(x+y)]dy/dx=e^(x+y)
dy/dx=[e^(x+y)]/[1-e^(x+y)]=1/[1-e^(x+y)]-1
d^2y/dx^2=[e^(x+y)*(1+dy/dx)]/[1-e^(x+y)]^2=[e^(x+y)]/[1-e^(x+y)]^3