求z^x-xyz=0所确定的z=f(x,y)的所有二阶偏导数
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设(y+z)/x=(x+z)/y=(x+y)/z=k;y+z=kx;x+z=ky;y+z=kx;2(x+y+z)=k(x+y+z);k=2或x+y+z=0;所以,(y+z)(x+z)(x+y)/xyz
令F=e^z-xyzF对x的偏导数为Fx=-yzF对z的偏导数为Fz=e^z-xy由偏导公式z对x的偏导=-Fx/Fz=yz/(e^z-xy)
设F(x,y,z)=sinz-xyz则F′(X)=-yzF′(y)=-xzF′(z)=cosz-xyz对x的谝导数等于-yz/(cosz-xy)z对y的谝导数等于-xz/(cosz-xy)dz=[-y
令(y+z)/x=(z+x)/y=(x+y)/z=t∴y+z=xt,z+x=yt,x+y=zt三式相加得:2(x+y+z)=(x+y+z)t∴(2-t)(x+y+z)=0∴2-t=0或x+y+z=0若
对y求导,e^z*z'(y)=xz+xyz'(y),əz/əy=z'(y)=xz/(e^z-xy)
两边微分e^zdz-yzdx-xzdy-xydz=0(e^z-xy)dz=yzdx+xzdy∂z/∂y=xz/(e^z-xy)=xz/(xyz-xy)=z/(yz-y)
x^2+y^2+z^2-3xyz=0两边对x求偏导,2x+2z*dz/dx-3yz-3xydz/dx=0从中解得:dz/dx=(3yz-2x)/(2z-3xy)(1)同理:dz/dy=(3xz-2y)
首先令(x,y,z)=x^3+y^3+z^3-3xyzgx=3x^2-3yzgz=3z^2-3xyzx=-(gx/gz)=-(3x^2-3yz)/(3z^2-3xy)=-(x^2-yz)/(z^2-x
方程两边对x求偏导:yz+xyəz/əx=(z+xəz/əx)e^xz得:əz/əx=(ze^xz-yz)/(xy-xe^xz)方程两边对y
对x求导,e^z*z'(x)=yz+xyz'(x),z'(x)=yz/(e^z-xy)对y求导,e^z*z'(y)=xz+xyz'(y),z'(y)=xz/(e^z-xy)
对X的偏导=yz/(e^z-xy)对Y的偏导=xz/(e^z-xy)
先对x求偏导数得z'(x)cosz=yz+z'(x)y所以z'(x)=yz/(cosz-y)同理对y求偏导数得z'(y)=xz/(cosz-x)所以dz=yz/(cosz-y)dx+xz/(cosz-
y^3z^2-x^2+xyz-5=0等式两边同时对x求导:∂z/∂x=(2x-yz)/(2zy^3+xy)等式两边同时对y求导:∂z/∂y=-(3y
我帮你做一步下面的你应该就会了,
记p=√(x^2+y^2+z^2),则xyz+p=√2,p=√2-xyz两边对x求偏导得:yz+xyz'(x)+[x+zz'(x)]/p=0得:z'(x)=(-yz-x/p)/(xy+z/p)=-(p