求xy=ex y的隐函数的导数
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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
这种题可以直接全微分,即e^xdx+xdy+ydx=0所以dy/dx=(e^x+y)/-x
Z=f'x(x,y)=xy*[x^(xy-1)]*yZ=f'y(x,y)=xy*[x^(xy-1)]*x再问:答案是Z=f'x(x,y)=yx^xy(lnx+1),Z=f'y(x,y)=x^(xy+1
z=xy+x/y对x的偏导数=y+1/y对y的偏导数=x-x/y^2
两边同时对X求导y+xy`=e^x+y`y`=(e^x-y)/(x-1)
xy³=y+xy³+3xy²*y'=y'+1(3xy²-1)y'=1-y³y'=(1-y³)/(3xy²-1)3y²y'
方程两边对变量x求导有d[sin(xy)]/dx=dx/dxcos(xy)*d(xy)/dx=1cos(xy)*(dx*y+x*dy)/dx=1cos(xy)*[y+x*(dy/dx)]=1所以:dy
先对X求导y+xy'-e^x+e^yy'=0y'=(e^x-y)/(x+e^y)再问:主要是e^y我不懂,答案是对的,老师。还有y'=0是为什么?
直接两边对x求导,得1/y*(-1/y2)*dy/dx=1/xy*(y+xdy/dx)下面会了吧
构造函数,F(X,Y)=xy-e^(xy)则dy/dx=-Fx/Fy=-[y-e(xy)*y]/[x-e^(xy)*x]
两边求导:e^(xy)*(xy)'-(xy)'=0e^(xy)*(y+xy')-(y+xy')=0ye^(xy)+xe^(xy)*y'=y+xy'x(e^(xy)-1)y'=y(1-e^(xy))y'
隐函数求导,就是先左右一起求微分,加个d,然后写出多少dx+多少dy=0,移项变成dy/dx=多少的形式就好了
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)
xy+lny=1两边求导y+xy'+y'/y=0y'=-y/(x+1/y)=-y^2/(xy+1)
令u=xy,则z对x的偏导就变为(dz/du)*(偏u/偏x),然后按这样的顺序算就行了,同理,对y也一样,不知道这样说你明不明白
解两边求导y‘cosy+e^x-y^2-2xyy'=0即y’(cosy-2xy)=y^2-e^xy'=(y^2-e^x)/(cosy-2xy)或者F(x,y)=siny+e^x-xy^2=0Fx=e^
两边分别求x的导数得:e^x+(y+xy')=0,即y'=-(e^x+y)/x,即:dy/dx=-(e^x+y)/x
z=y+cosx+x再问:偏导数,不是导数再答:这不就是偏导数吗再问:哦,有全过程吗,谢谢再答:ðz/ðx=y+cosxðz/ðy=x
答:1)y/x=ln(xy^2)两边求导:y'/x-y/x^2=[1/(xy^2)]*(y^2+2xyy')(xy'-y)/x=(y+2xy')/yy'-y/x=1+2xy'/y(1-2x/y)y'=
e^(x+y)=xy两边对x求导:e^(x+y)*(1+y')=y+xy'解得:y'=[y-e^(x+y)]/(e^(x+y)-x]=(y-xy)/(xy-x)