z＝e^(x^2 y^2) z(xy)＝

∑是循环和例如∑a=a+b+c∑a^2=a^2+b^2+c^2∑(z-y)(x-y)/(x+y-2z)(y+z-2x)＝∑(z-y)(x-y)(x+z-2y)/(x+y-2z)(y+z-2x)(x+z

有这样的公式：a^3+b^3+c^2-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)左边减右边,证明：（x+y-2z)^3+(y+z-2x)^3+(z+x-2y)^3-3（x+y

e^(-xy)-2z+e^z=0-ye^(-xy)-2z'(x)+e^zz'(x)=0z'(x)=ye^(-xy)/(e^z-2)-xe^(-xy)-2z'(y)+e^zz'(y)=0z'(y)=xe

x2-(y+z)2=(x+y+z)(x-y-z)=8x+y+z=2所以x-y-z=8÷2=4

对方程e^(-xy)+2z-e^z=2两边微分,有：e^(-xy)*d(-xy)+2*dz-e^z*dz=0-e^(-xy)*(x*dy+y*dx)+2*dz-e^z*dz=0移项,得：(e^z-2)

∵x-2y+z=（x-y）-（y-z）,x+y-2z=（y-z）-（z-x）,y+z-2x=（z-x）-（x-y）．设x-y=a,y-z=b,z-x=c,则原式=-ac/(a-b)(b-c)+(-ba

正整数?取对数即证：2xlnx+2ylny+2zlnz>(y+z)lnx+(x+z)lny+(x+y)lnzx>y>z,lnx>lny>lnz由排序不等式得xlnx+ylny+zlnz>ylnx+zl

偏导真不好写呀偏z/偏y=x^2*e^y偏(偏z/偏y)/偏y=x^2*e^y

两端对x求偏导得：-ye^(-xy)-2(z/x)+(z/x)e^z=0,所以,z/x=ye^(-xy)/(e^z-2)两端对y求偏导得：-xe^(-xy)-2(z/y)+(z/y)e^z=0,所以,

(y+z-2z)这步有错吧

1、隐函数对x求导得1+az/ax+yz+xy*az/ax=0,故az/ax=－(1+yz)/(1+xy)；F对x求导得aF/ax=e^x*y*z^2+e^x*y*2z*az/ax；当x＝0,y＝1时

由已知得dy/dx=(e^y+z)/(e^x+z),dz/dx=(z^2-e^(x+y))/(e^x+z),dz/dy=(z^2-e^(x+y))/(e^y+z),所以可以得到三式,e^ydx+zdx

2x+y+3z＝38①3x+2y+4z＝56②4x+y+5z＝66③③-①得：2x+2z=28，即x+z=14④，①×2-②得：x+2z=20⑤，由④和⑤组成方程组：x+z＝14x+2z＝20，解得：

x+2y+z=e^(x-y-z)两边对x求偏导注意到z=z(x,y)1+z'=e^(x-y-z)*(1-z')...(1)再对x求偏导z"=e^(x-y-z)(1-z')^2-z"e^(x-y-z).

第二个分母写错了?(y-x)(z-x)/(x-2y+z)/(x+y-2z)+(z-y)(x-y)/(x+y-2z)/(y+z-2x)+(x-z)(y-z)/(y+z-2x)/(x-2y+z)=1

(y+z-x)/{x^2-(y+z)^2}=(y+z-x)/[(x-y-z)(x+y+z)]=-(x-y-z)/[(x-y-z)(x+y+z)]=-1/(x+y+z)

=x²(y-z)+y²(z-x)+z²(x-z+z-y)=(y-z)(x²-z²)+(z-x)(y²-z²)=(y-z)(x-z)

3元一次方程,好像是初一的问题哦.根据前面两个等式可以得出x=3zy=z(平方)/32x+3y+4z=2*(3z)+3*(z方/3)+4z现在变成了一元二次方程,你应该会解吧.

x^4(y-z)+y^4(z-x)+z^4(x-y)=xy(x^3-y^3)+yz(y^3-z^3)+zx(z^3-x^3)=xy(x^3-y^3)+yz(y^3-z^3)-zx[(x^3-y^3)+

根据公式(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ac公式展开：得到(x^2+y^2+z^2=2xy-2yz-2xz)-(x^2+y^2+z^2-2xy-2yz+2xz)合并同类项