函数z=x² y²的全微分dz
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![函数z=x² y²的全微分dz](/uploads/image/f/2328263-71-3.jpg?t=%E5%87%BD%E6%95%B0z%3Dx%C2%B2+y%C2%B2%E7%9A%84%E5%85%A8%E5%BE%AE%E5%88%86dz)
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/∂x=2xy∂z/∂u=x²所以dz=2xydx+x²dy
xyz=x+y+z所确定的函数z(x,y)的全微分dz两端求微分得yzdx+xzdy+xydz=dx+dy+dz这里z是看成自变量,即x,y,z都是独立的.再问:两边同时求对x的偏导数时,z看成中间变
z'x=2e^(2x+y)z'y=e^(2x+y)所以dz=2e^(2x+y)dx+e^(2x+y)dy
全微分的定义:函数z=f(x,y)的两个偏导数f'x(x,y),f'y(x,y)分别与自变量的增量△x,△y乘积之和,即为f'x(x,y)△x+f'y(x,y)△y,若该表达式与函数的全增量△z之差在
解;z(x)=2x+2y²z(y)=4xy+12y²dz=(2x+2y²)dx+(4xy+12y²)dy
D.是f(x,y)的极小值点
dz=[-3ysin3xy+1/(1+x+y)]dx+[-3xsin3xy+1/(1+x+y)]dy
z偏x=-sin3xy*3y+1/(x+y+1)z偏y=-sin3xy*3x+1/(x+y+1)dz=[-sin3xy*3y+1/(x+y+1)]dx+[sin3xy*3x+1/(x+y+1)]dy
两边对x求导:Z'xlnx+Z/x=y*Zx/z,得:Z'x=Z/x/(y/z-lnx)两边对y求导:Z‘ylnx=lnz+y*Z'y/z,得:Z'y=lnz/(lnx-y/z)dz=Z'xdx+Z'
再问:非常感谢,还要问大侠一道题面目。曲线y=x³+3x的拐点坐标为???再答:y'=3x²+3y''=3x令y"=0,得x=3当x=3时,y=36所以拐点坐标(3,36)
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)
http://hi.baidu.com/fjzntlb/album/item/ef8139f61e7f7842730eec56.html#
dz=Z'xdx+Z'ydy=2xcos(x^2+y^2)dx+2ycos(x^2+y^2)dy
dz=[2e^(2x+y)]dx+[e^(2x+y)]dy
再问:啊不好意思搞错了。。是z=e^(x^2+y^2),求dz,谢谢你帮我解答一下吧。。再答:
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.
z=x^3y^2dz=3x^2*y^2dx+2x^3*ydy,在(1,1)处的全微分dz=3dx+2dy.
dz=x的偏导数乘德尔塔x+y的偏导数乘德尔塔y这是最基础的题呀,直接套公式啊