求x^2 y^2-xy=1所确定的隐函数y=y(x)的导数dy dx

方程两边同时求x对y的导：y+xdy/dx+1/x+2ydy/dx=0,dy/dx=-(y+1/x)/(x+2y),dy=-(y+1/x)dx/(x+2y)

由隐函数求导法可得dy/dx=-(2x-y)/(2y-x)根据复合函数的链式求导法则可得dz/dx=2x+2y*dy/dx=2x-2y(2x-y)/(2y-x)=2(y²-x²)/

xy+e^y=y+1（1）求d^2y/dx^2在x=0处的值：（1）两边分别对x求导：y+xy'+e^yy'=y'y/y'+x+e^y=1(2)(2)两边对x再求导一次：(y'y'-yy'')/y'^

隐函数求导设z=x²y²-cos(xy)dy/dx=-(δz/δx)/(δz/δy)=-(2xy²+ysin(xy))/(2x²y+xsin(xy))=-y/x

-sin(xy)[ydx+xdy]=2xy^2*dx+x^2*2ydy-sin(xy)ydx-sin(xy)xdy=2xy^2*dx+2x^2*ydy-2x^2*ydy-sin(xy)xdy=2xy^

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-2x

1）y|x=o当x=0时sin(0)-1/y-0=1得：y|x=0=-1(2)y'|x=osin(xy)-1/y-x=1两边对x求导：cos(xy)(y+xy')+y'/y^2-1=0当x=0时y=-

2xdx+ydx+xdy+2ydy=0(x+2y)dy=-(2x+y)dxdy=-(2x+y)/(x+2y)×dx

e^(xy)(y+xdy/dx)-4x-dy/dx=0；dy/dx(xe^(xy)-1)=-ye^(xy)+4x；dy/dx=(4x-ye^(xy))/(xe^(xy)-1).

1、两边同时微分,y^3dx+3xy^2dy=dy,sody/dx=(y^3)/(1-3xy^2)2、dy=(e^x)/(1+e^(2x))dx

不对.方程同时对X求导有3x^2+3y^2y'=4y+4xy'得到y'=(4y-3x^2)/(3y^2-4x)x=2时y=2y'(2)=(4*2-3*2^2）/(3*2^2-4*2)=-1

dz/dx=dz/dx+dz/dy*dy/dx.然后你就知道了,高数中的链式法则啊.

dy²-2d(xy)+0=02ydy-2(xdy+ydx)=02ydy-2xdy=2ydxdy/dx=y/(y-x)

1)x=0代入方程：1-e^y=0,得y(0)=0两边对X求导：e^x-y'e^y=cos(xy)(y+xy')y'=[e^x-ycos(xy)]/[xcos(xy)+e^y]代入x=0,y(0)=0

求导得：6y²y'-4yy'+2y+2xy'-2x=03y²y'-2yy'+y+xy'-x=0y‘(3y²-2y+x)=x-yy'=(x-y)/(3y²-2y+

2x+2y+2xy'-2yy'=2y'(x-y)=1-x-ydy/dx=(1-x-y)/(x-y)

对y^2－2xy＝7求微分,得2ydy-2(ydx+xdy)=0,∴（y-x)dy=ydx,∴dy/dx=y/(y-x).

xy+e^y=1e^y(0)=1y(0)=0xy'+y+e^yy'=00+y(0)+y'(0)=0y'(0)=0xy''+y'+y'+e^yy''+(y')^2e^y=00+2y'(0)+y''(0)

设dy/dx=y'.求导,2yy'-2y-2xy'=0dy/dx=y'=y/(y-x)

第一步方程两边对x求导记y+xy'-y'/y=2x第二步解出y'记y'=(2xy-y^2)/(xy-1)