(x^3+xy^2+1)/(x^3+xy^2-x^2y-y^3)×(x^2y-xy^2)/(x^3+xy^2-x^2y-

-4x²·(½xy-y²)-3(xy²-2x²y)
=-2x³y+4x²y²-3xy²+6x²y /化简的话,到此结束,因式分解的话,继续：
=-xy(2x²-2xy+3y-6x)

x^4-y^4+ 3xy^2-x^2y-2xy^2+2y^4
= (x^2)^2-(y^2)^2+xy(3y-x-2y)+2(y^2)^2
=(x^2)^2+(y^2)^2+xy(y-x)
=10

1/x+1/y+1/z=1/x³+1/y³+1/z³+3/(x²y)+3/(xy²)+3/(x²z)+3/(xz²)+3/(y²z)+3/(yz²)+6/(xyz)
1/x+1/y+1/z=(1/x+1/y+1/z)³
(1/x+1/y+1/z)³-(1/x+1/y+1/z)=0
(1/x+1/y+1/z)[(1/x+1/y+1/z)²-1]=0
(1/x+1/y+1/z)(1/x+1/y+1/z +1)(1/x+1/y+1/z -1)=0
1/x+1/y+1/z=0或1/x+1/y+1/z=-1或1/x+1/y+1/z=1
题目不难啊,关键是要知道：
1/x³+1/y³+1/z³+3/(x²y)+3/(xy²)+3/(x²z)+3/(xz²)+3/(y²z)+3/(yz²)+6/(xyz)=(1/x+1/y+1/z)³

原式=(2x³y-2x²y²+2x²y²-x³y)÷x²y
=x³y÷x²y
=x
=2008

这是隐含数求导,两边先对 x 求导,
e^x=-y'siny-(y^2+x2yy'),整理得
y'=-(y^2+e^x)/(siny+2xy),把 x=0 代入,得
y'|x=0=-(y^2+1)/siny ,是不是这样?

5xy²-[3xy²-(4xy²-2x²y)]+2x²y-xy²
=5xy²-（3xy²-4xy²+2x²y）+2x²y-xy²
=5xy²-(-xy²+2x²y)+2x²y-xy²
=5xy²+xy²-2x²y+2x²y-xy²
=(5xy²+xy²-xy²)+(-2x²y+2x²y)
=5xy²

δz/δv =δz/δx *δx/δv +δz/δy *δy/δv=(2xy-y^2)(-usinv)+(x^2-2xy)ucosv
δz/δu =δz/δx *δx/δu +δz/δy *δy/δu=(2xy-y^2)cosv+(x^2-2xy)sinv

-2y^3+(3xy^2-x^2y)-2(xy^2-y^3)
原式=-2y^3+3xy^2-x^2y-2xy^2+2y^3
=xy^2-x^2y

是要化简吗?
-2y^3+(3xy^2-x^2y)-2(xy^2-y^3)
=-2y^3+(3xy^2-x^2y)-2xy^2+2y^3(合并同类项)
=xy^2-x^2y（提取公因式）
=xy（y-x）

xy^2-x^2 *y=xy(y-x)=-30 （x+y）^2=x^2+y^2+2xy=(x-y)^2+4xy=25+24=49