两边对x求偏导
e^z*z'(x)=y(z+x*z'(x))
z'(x)=yz/(e^z-xy)
∂z/∂x=yz/(e^z-xy)
原式对y求偏导
e^z*z'(y)=x(z+y*z'(y))
∂z/∂y=xz/(e^z-xy)
dz=∂z/∂x*dx+∂z/∂y*dy
=yz/(e^z-xy)*dx+xz/(e^z-xy)*dy
1.设z=z(x,y)是由方程式e的z次方=xyz所含的隐函数,求dz 2.计算出曲面z...
（1）e^z=xyz，等式两端分别微分：(e^z)dz=(xy)dz+(xz)dy+(yz)dx；(e^z -xy)dz=(yz)dx+(xz)dy；dz=[yz\/(e^z-xy)]dx+[xz\/(e^z-xy)]dy=[z\/(xz-x)]dx+[z\/(yz-y)]dy；（2）曲面 z=2-x²-y² 为一伞形曲面，当 z=2 时，x=y=0；当 z=0（xoy ...
设Z=f(x,y)是由方程e的z次方=xyz所确定的函数 求dz
d(e^z)=d(xyz)e^zdz=yzdx+xzdy+xydz (e^z-xy)dz=yzdx+xzdy dz=(yzdx+xzdy)\/(e^z-xy)=yz\/(e^z-xy)dx+xz\/(e^z-xy)dy
设函数z=z(x,y)是由方程z+e的z次方=xy所确定的隐函数,求全微分dz.
令F(x，y，z）= z+z^e-xy=0 ∴Fx=y Fz=-1+e^z，有隐函数订立Z先对x偏导=y\/1+e^z ∴Fy=x 有隐函数订立Z先对y偏导=x\/1+e^z 所以Z先对x再对y求偏导(y\/1+e^z)dx+(x\/1+e^z)dy 意义：微积分学的创立，极大地推动了数学的发展，过去很多用初等数学无法解决的问题...
设z=z(x.y)是由方程x+y+z=e的z次方所确定,求dz
dz\/dx=-Fx\/Fz=1\/(e^z-1),dz\/dy=-Fy\/Fz=1\/(e^z-1),dz=1\/(e^z-1) * (dx+dy)
设z=Z(x,y)是由方程x+Y+z=(e的x次方)所确定的隐函数,求dz
题目：x+y+z=e^x dx+dy+dz=e^xdx dz=[(e^x)-1]dx-dy
设z=f(x,y)是由方程x+Y+z=(e的x次方)所确定的隐函数,求dz,
以下用D表示求偏导数.对式子两边求偏导得 (视y为常数)1+Dz\/Dx=e^x (视x为常数)1+Dz\/Dy=0 故dz=(Dz\/Dx)dx+(Dz\/Dy)dy =(e^x-1)dx-dy.
z=z(x,x\/y)由方程z+e的z次方=xy所确定的隐函数,求αz\/αx,αz\/αy
z+e^z=xy dz+e^z*dz=ydx+xdy (1+e^z)dz=ydx+xdy 所以：αz\/αx=y\/(1+e^z)αz\/αy=x\/(1+e^z)
设Z的X次方=Y的Z次方所确定的隐函数Z=Z(X,Y),求DZ\/Dx
如图
...设z=z(x,y)由方程e的z次方-xy的2次方+sin(y+z)=0确定,求dz_百度知 ...
用最基本的方法计算如下：令F(x,y,z)=e^z-xy²+sin(y+z)则 F'x=-y²,F'y=-2xy+cos(y+z),f'z=e^z+cos(y+z)于是Z'x=-(-y²)\/[e^z+cos(y+z)],Z'y=-[-2xy+cos(y+z)]\/[e^z+cos(y+z)],dz=Z'xdx+Z'ydy ={y²dx+[2xy-cos(y+z)]...
...设z=z(x,y)由方程e的z次方-xy的2次方+sin(y+z)=0确定,求dz_百度知 ...
设F＝e^z-xy^2+sin(y+z)F分别对x、y、z求导 Fx^'=-y^2 Fy^'=-2xy+cos(y+z)Fz^'=e^z+cos(y+z)Z对x的偏导数为-Fx^'\/Fz^'＝y^2\/[e^z+cos(y+z)]Z对y的偏导数为-Fy^'\/Fz^'＝-[-2xy+cos(y+z)]\/[e^z+cos(y+z)]＝[2xy-cos(y+z)]\/[e^z+cos(y+z)]dz...
