z=ln(u v),u=e的x y次方

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

1.az/ax=1/2*1/√ln(xy)*1/(xy)*y=1/(2x√ln(xy))同理：az/ay=1/(2y√ln(xy))2.au/am=1/(1+(m^2n)^2)*n*2m=2mn/(1

δz/δx=1/(xy+x/y)*(y+1/y)=(y²+1)/(xy²+x)=1/xδ^2z/δxδy=δ(δz/δx)/δy=0

dz=d(xyln(xy))=xyd(ln(xy))+ln(xy)d(xy)=xyd(xy)/(xy)+ln(xy)d(xy)=d(xy)+ln(xy)d(xy)=(1+ln(xy))d(xy)=(1

UV=acXY+adX+bcY+bdE(UV)=acE(XY)+adEX+bcEY+bdEU=aEX+bEV=cEY+dEU*EV=acEXEY+adEX+bcEY+bd因此两式相减得E(UV)=EU

1.函数f(x,y)=ln(y-x)+1/√(y+x)的定义域?y>x,且y>-x2.如果函数z=sinvlnu,u=x+y,v=xyz=sin(xy)ln(x+y)3.设z=arctan

z=f(x,u),u=xy,求z对x的二阶偏导数∂z/∂x=∂f/∂x+(∂f/∂u)(∂u/∂x)=&

嗯,是对的

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

其实很简单,只不过是一种运算的方法（可以跟a（bc）=abac类比）.y=uv,y再问：什么

将e^(u+v)=uv两边对u求导得：　　e^(u+v)*(1+v')=v+u*v'　　解得v'=(v-e^(u+v))/(e^(u+v)-u)　　即dv/du=(v-e^(u+v))/(e^(u+v

u=ln(xy+z)du=d[ln(xy+z)]/dx*dx+d[ln(xy+z)]/dy*dy+d[ln(xy+z)]/dz*dz=y/(xy+z)*dx+x/(xy+z)*dy+1/(xy+z)*

z=(x^2)*ln(2xy),Zx=(2x)ln(2xy)+(x^2)/2xy*(2xy)'=(2x)ln(2xy)+xZxx=2ln(2xy)+(2x)/2xy*(2xy)'+1=2ln(2xy)

dy/dx=dy/du*du/dx+dy/dv*dv/dx=v*e^(x+y)+u*y/x=ln(xy)*e^(x+y)+e^(x+y)*y/x=e^(x+y)[ln(xy)+y/x]所以dy=e^(

说明：eu应该是e的x次幂,dz/dx,dz/dy应该是偏导数.∵v=xy,u=x2-y2∴du/dx=2x,du/dy=-2y,dv/dx=y,dv/dy=x∵z=ln(e^u+v),∴dz/dx=

①偏z/偏x=偏z/偏u偏u/偏x+偏z/偏v偏v/偏x=(2uv-v^2)siny+(2uv-v^2)cosy=(2x^2sinycosy-x^2(cosy)^2)siny+(2x^2sinycos

两边求导得y'·e^y+(y+xy')/(xy)+e^(-x)=0

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)

z=u²v+3uv^4,u=e^x,v=sinx,求dz/dxdz/dx=2uu'v+u^2v'+3u'v^4+3v(4v^3)v'=2e^(2x)sinx+e^(2x)cosx+3e^x(

对等式两边求全微分du=【1/(2x+3y+4z^2)】【2dx+3dy+8zdz】