y*y-2xy 10=0所确定的隐函数的导数是什么

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'^

第一题,这是个隐函数,两边对x求导得：2y'-1=(1-y')*ln(x-y)+(x-y)*(1-y')/(x-y)=(1-y')*ln(x-y)+(1-y')所以[3+ln(x-y)]y'=ln(x

y^2/（x+y）=y^2-x^2y^2=（y^2-x^2）（x+y）两边同时求导得到：2yy’=(2yy’-2x)(x+y)+(y^2-x^2)(1+y’)2yy’=2yy’(x+y)-2x(x+y

两边对x求导2xy+x^2y'-(1+y^2)^(1/2)*y'=0前面两项是对于原方程的第一项运用积法则+链式法则得来的整理可得y'=2xy/[(1+y^2)^(1/2)-x^2]

两边对x求两次导数：1-y'+1/2cosyy'=0；==>y'=1/(1-cosy/2)0-y''+1/2(y'(-siny)+cosyy'')=0==>y''=y'siny/(cosy-2)再将y

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

∵2x²y-xy²+y³=0==>4xydx+2x²dy-y²dx-2xydy+3y²dy=0==>(4xy-y²)dx=(2xy

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

原方程是xy=1-e^y?如果是的话将等式两边对X求导数得y+xy'=e^y*y'则y‘=y/(e^y-x)y'(0)=y/e^y

两边对x求导：2-y'=(y'-1)ln(y-x)+(y-x)*1/(y-x)*(y'-1)=(y'-1)[ln(y-x)+1]2-y'=y'[ln(y-x)+1]-[ln(y-x)+1]y'[ln(

xy'+y+sin(πy)πy'=0y'=-y/[x+πsin(πy)]

y'=-2sin2(x+y)-2y'sin2(x+y)(1+2sin2(x+y))y'=-2sin2(x+y)y'=-2sin2(x+y)/(1+2sin2(x+y))

x-y+1/2siny=0F(x,y)=y-x-1/2siny=0F,Fx,Fy在定义域的任意点都是连续的,F(0,0)=0Fy(x,y)>0f'(x)=-Fx(x,y)/Fy(x,y)=1/(1-1

（0,-1）在曲线上,是切点对x求导cos(x²y)*(2xy+x²*y')+1/(2x-y)*(2-y')=0吧(0,-1)代入2-y'=0所以切线斜率k=y'=2所以是2x-y

将y看作是x的函数,则对x求导数有：3y^2*y'-3y'+2=0求出y'=2/3(1-y^2)其中y^2,y^3表示幂函数

.y/x=ty=txy=xtdy/dx=t+t'xdy=(t+t'x)dxy^2(x-y)=x^2t^2(x-tx)=1x=1/[t^2(1-t)]y=1/[t(1-t)]1/y^2=t^2(1-t)

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

两边对x求导,则2x-[e^y+x(e^y)y']=0整理得y'=(2x-e^y)/(xe^y)

e^y-e^x=xy两边求导,得e^y*y'-e^x=y+xy'(e^y-x)y'=(e^x+y)所以y'=(e^x+y)/(e^y-x)x=0时,e^y-e^0=0,则e^y=1,则y=0所以y'(

微分得xe^ydy+e^ydx+2ydy=0,解得dy/dx=-e^y/(xe^y+2y)