求下列函数的全微分z=e^y x-搜答案-搜搜做题作业网

我来试试吧...z=e^xy*cos(x+y)Z'x=ye^xycos(x+y)-e^xysin(x+y)Z'y=xe^xycos(x+y)-e^xysin(x+y)故dZ=[ye^xycos(x+y

Z=（1/2）ln(1+x²+y²)dz=(1/2)2x/(1+x²+y²)dx+(1/2)2y/(1+x²+y²)dy=x/(1+x&su

z'x=2e^(2x+y)z'y=e^(2x+y)所以dz=2e^(2x+y)dx+e^(2x+y)dy

Z=e^xy在x处的导函数为ye^(xy)在y处的导函数为xe^(xy)dz=ye^(xy)dx+xe^(xy)dy=2e^2dx+e^2dy

对方程两边求全微分得：(e^z-1)dz+y^3dx+3xy^2dy=0（方法和求导类似）移项,有dz=-(y^3dx+3xy^2dy)/(e^z-1)

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

z=3x²y+x/yzx=6xy+1/yzy=3x²-x/y²所以dz=zxdx+zydy=(6xy+1/y)dx+(3x²-x/y²)dy

他说的方法对但算的好像不对,高数扔好久了,我试试哈,dz=y*(1/x^2)*e^(y/x)*dx+(1/x)*e^(y/x)*dy.另外,我不知道是不是你手误,我给出的答案是按照z=e^(y/x)算

代入：2z-2z+lnz=0--->z=1,所以z'(y)=-z/y从而dz=z'(x)dx+z'(y)dy=(e^x-yz)/(xy)

两边即对数得：lnz=xy*ln(lnu),不妨记u=x^2+y^2z'x/z=yln(lnu)+2x^2y/lnu,z'x=z[yln(lnu)+2x^2y/lnu]z'y/z=xln(lnu)+2

1.z'x=3x²y²z'y=2x³y2.z'x=4x³z'y=3y³3.z'x=ye^(xy)+2xyz'y=xe^(xy)+x²4.u'

dz=2e^(2x+y^2)dx+2ye^(2x+y^2)dy把对x和对y的偏导分别求了出来再乘以各自的微分项即可.

u'x=2x/(x^2+y^2+z^2)u'y=2y/(x^2+y^2+z^2)u'z=2z/(x^2+y^2+z^2)du=2xdx/(x^2+y^2+z^2)+2ydy/(x^2+y^2+z^2)

dz=1/y/(1+x^2/y^2)*dx-x/y^2/(1+x^2/y^2)*dy

先求出z对x和y的偏导数分别是1/y,-x/y^2所以dz=(1/y)*dx-(x/y^2)*dy

dz=2xydx+x^2dy再问：有全过程吗再答：en我想知道这里的X^2Y是指的X得平方乘以Y吗？如果是过程如下：dz/dx=2xydz/dy=x^2dz=2xydx+x^2dy再问：是X的2Y次方

dz=(y+1/y)dx+(x-x/y^2)dy