求曲线y=Ln(x y)所确定的隐函数的导数y·x-搜答案-智慧作业帮

sin(xy)+ln(y-x)=x两边同时对x求导得：cos(xy)·(y+xy')+(y'-1)/(y-x)=1①当x=0时,sin0-lny=0,解得y=1把x=0,y=1代入①得：cos0·(1

方程两边求关x的导数ddx(xy)＝(y+xdydx)； ddxex+y＝ex+y(1+dydx)；所以有（y+xdy

令F（x,y)=cos(xy)-x-yF'(x,y)x=-ysin(xy)-1对x求偏导F'(x,y)y=-xsin(xy)-1对y求偏导切线方程为：（x-0)/F'(x,y)=(y-1)/F'(x,

两条渐近线,一条是x=1/e,另一条是y=1

直接在等式中零,x=0,y=y（0）,可得关于y（0）的方程解出y（0）即可.具体：e^0*y(0)+lny(0)/1=0即-y（0）=lny（0）作图y1=-x,y2=ln（x）,两者的交点的横坐标

两边对x求导得y+xy'=(1+y')/(x+y)y(x+y)+x(x+y)y'=1+y'y'[x(x+y)-1]=1-y(x+y)y'=[1-y(x+y)]/[x(x+y)-1]dy=[1-y(x+

两边微分cosydy=(dx+dy)/(x+y)[cosy(x+y)-1]dy=dxdy/dx=1/[cosy(x+y)-1]

F(x,y)=x+lny-y=0dF(x,y)=0=(∂F(x,y)dx/∂x)+(∂F(x,y)dy/∂y)dy/dx=-(∂F(x,y)

设Y=y'降阶：Y'=(Y/x)ln(Y/x)这就是一个一阶齐次方程.设Y/x=u,所以Y=ux,Y'=u+x(du/dx),代回原方程,解得：lnu=C1x+1Y=xe^(C1x+1)所以y=[(C

y'=(y+xy')/(xy)xyy'-xy'=yy'=y/(xy-x)所以dy/dx=y'=y/(xy-x)

x=yln(xy)dx=d(yln(xy))=ln(xy)dy+(y/(xy))d(xy)=ln(xy)dy+(1/x)(ydx+xdy)=ln(xy)dy+(y/x)dx+dy合并同类项有(ln(x

xy'+y+sin(πy)πy'=0y'=-y/[x+πsin(πy)]

先求导等式两边同时对x求导得y+xy'+y'/y=0则y'=-y^2/(xy+1)当x=1,y=1时,y'=-1/2故切线方程为y-1=-1/2(x-1)即x+2y-3=0

[ln(xy)]'=[e^(x+y)]'(xy)'/(xy)=e^(x+y)*(x+y)'(y+xy')/(xy)=e^(x+y)*(1+y')y'=y[e^(x+y)-1]/[x(1-ye^(x+y

y+xy'+y'/y=0//对xy和lny分别求导,注意y是x的函数y'(x+1/y)=-y//移项,合并同类项y'=-y²/(xy+1)

两边求导e^y×y'=xy'+yy'=y/(e^y-x)dy/dx=y/(e^y-x)

还用求吗?只有一条渐近线x=-1.又因x趋于正无穷大时,y'=0,但直线y=c无论c取何值与y=ln(1+x)均有交点,故x趋于正无穷大没有渐进线.

xe^f(y)=ln2009e^ye^f(y)+xe^f(y)*f'(y)*y'=y'e^f(y)(1+xf'y')=y'e^f*f'*y

ln（xy）=e^x+ylnx+lny=e^x+y两边同时对x求导1/x+(1/y)(dy/dx)=e^x+dy/dxdy/dx=[(1/x)-e^x]/[1-(1/y)]=(y-xye^x)/(xy

min是指f(x)g(x)h(x)三个函数中的最小值