设函数y=y(x)由方程x^2y^2+y=1(y>0)所确定求dy/dx|x=0,d^2y/dx^2|x=0.

来源：学生作业帮编辑：大师作文网作业帮分类：数学作业时间：2024/11/11 18:28:53

∵x²y²+y=1(y>0)
==>2xy²+2x²yy'+y'=0 (等式两端对x求导数).(1)
==>2y²+4xyy'+4xyy'+2x²(yy''+y'²)+y''=0 (等式两端对x求导数).(2)
∴由(1)得y'=-2xy²/(2x²y+1)
由(2)得y''=-(2y²+8xyy'+2x²y'²)/(2x²+1)
∵当x=0时,y=1
∴dy/dx|(x=0)=y'|(x=0)=-2*0*1²/(2*0²*1+1)=0
d²y/dx²|(x=0)=y''|(x=0)=-(2*1²+8*0*1*0+2*0²*0²)/(2*1²+1)=-2/3.

设函数y=y(x)由方程x^2y^2+y=1(y>0)所确定求dy/dx|x=0,d^2y/dx^2|x=0. 设函数y=y(x)由方程y+e^(x+y)=2x确定,求dx/dy 设y=y(x)是由方程xy+e^y=y+1所确定的隐函数,求d^2y/dx^2 x=0 设函数 y=y(x) 由方程y平方－２xy＝７所确定求 dy／dx 设函数y=y(x)由方程x^2+y^2=1确定,求dy/dx 设函数y=y（x）由方程x^2+y^2=1确定,求dy/dx 设函数y由方程ln y+x/y=0确定,求dy/dx 设函数y=y(x)由方程y=xe^y确定,求dy/dx和d^2/dx^2 设函数y=y(x)由x=1-e^t和y=t+e^-t确定,求dy/dx和d^2y/dx^2 设函数y=y(x)由方程ln(x^2+y^2)^1/2=arctany/x所确定,求dy/dx. 设函数y=y(x)由方程(x+y)^(1/x)=y所确定,则dy/dx=? 设函数y＝y(x)由方程y＋e的(x+y)次方=2x所确定,求dy/dx,d＾2y/dx＾2.

设函数y=y(x)由方程x^2y^2+y=1(y>0)所确定 求dy/dx|x=0,d^2y/dx^2|x=0.

设函数y=y(x)由方程x^2y^2+y=1(y>0)所确定求dy/dx|x=0,d^2y/dx^2|x=0.