z=f(x,y) xy+yz+xz=1 ,求dz
来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/11/11 14:20:35
z=f(x,y) xy+yz+xz=1 ,求dz
dz=(∂ z / ∂ x)dx+(∂ z / ∂ y)dy
xy+yz+xz-1=0
设g(x,y,z)=xy+yz+xz-1
∂ g / ∂ x =y+z ①
∂ g / ∂ y =x+z ②
∂ g / ∂ z =x+y ③
∂ z / ∂ x = - ①/③= -(y+z)/(x+y)
∂ z / ∂ y = - ②/③= - (x+z)/(x+y)
所以
d z = -(y+z)d x /(x+y)- (x+z)dy /(x+y)
= - [(y+z)d x +(x+z)d y ] /(x+y)
xy+yz+xz-1=0
设g(x,y,z)=xy+yz+xz-1
∂ g / ∂ x =y+z ①
∂ g / ∂ y =x+z ②
∂ g / ∂ z =x+y ③
∂ z / ∂ x = - ①/③= -(y+z)/(x+y)
∂ z / ∂ y = - ②/③= - (x+z)/(x+y)
所以
d z = -(y+z)d x /(x+y)- (x+z)dy /(x+y)
= - [(y+z)d x +(x+z)d y ] /(x+y)
z=f(x,y) xy+yz+xz=1 ,求dz
设方程xz+yz+xy=e的定函数z=z(x,y),求dz
x+y+z=5,xy+xz+yz=1 ,求Z的最小值和最大值
设z=z(x,y)由方程xy+yz-e^xz=0确定,则dz=
z=z(x,y)由方程x=f(xz,yz)确定其中f具有一阶连续偏导数求dz
f(x,y,z)=yz+xz使得,y^2+z^2=1,yz=3,求f最大值
设Z=f(xz,z/y)确定Z为x,y的函数求dz
求方程组的正整数解:x√(yz)+y√(xz)=39-xy y√(xz)+z√(xy)=52-yz z√(xy)+x√(
设方程f(xz,yz)=0可确定z是x,y的函数,且f(u,v)具有连续偏导数,求dz,
已知xyz=1,求x/(xy+x+1)+y/(yz+y+1)+z/(xz+z+1)的值
已知x+y+z=1,x²+y²+z²=2求xy+yz+xz的值
x-3=y-2=z-1,求x^2+y^2+z^2-xy-yz-xz的值