z=sin2xy y^2微分
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∂z/∂x=2xy∂z/∂u=x²所以dz=2xydx+x²dy
z'x=2e^(2x+y)z'y=e^(2x+y)所以dz=2e^(2x+y)dx+e^(2x+y)dy
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
x^2+y^2+z^2+4z=02xdx+2ydy+2zdz+4dz=0(2z+4)dz-2xdx-2ydydz=(-2xdx-2ydy)/(2z+4)
设F(x,y,z)=z^2-2xyz-1则Fx=-2yz,Fy=-2xz,Fz=2z-2xyαz/αx=-Fx/Fz=-(-2yz)/(2z-2xy)=yz/(z-xy)αz/αy=-Fy/Fz=xz
z=f(x,y∧2,z)两边取全微分,dz=f'xdx+(f'y)*2ydy+f'zdz所以dz=[(f'x)/(1-f'z)]dx+[2y(f'y)/(1-f'z)]dy
偏z/偏x=1/2根号(1-x^2-y^2)×(-2x)偏z/偏y=1/2根号(1-x^2-y^2)×(-2y)所以dz=[1/2根号(1-x^2-y^2)×(-2x)]dx+[1/2根号(1-x^2
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)
dz=2xdy+2ydx
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
zx=[√(x²+y²)-x²/√(x²+y²)]/(x²+y²)=y²/(x²+y²)^(3/2)
dz/dx=-3/2*(x^2+y^2)^(-3/2)*2x=-3x*(x^2+y^2)^(-3/2)dz/(dxdy)=-3x*(-3/2)*(x^2+y^2)^(-5/2)*2y=9xy*(x^2
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:
zx=2xzy=3y²dz=2xdx+3y²dy再问:谢谢!再问这位大侠一题若函数u(x,y)=y/x则du|(1,1)=?注:(1,1)在|的右下角再答:ux=-y/x²
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)
2^(x^2+y^2)*In2*(2xdx+2ydy)
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