ln求全微分
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嗯算是吧~比如Z=Z(X,Y)全微分的定义就是函数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f'x(x,y)△x+f'y(x,y)△y若该表达式
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
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
Zxe^z=YZ+XYZx,Zx=YZ/(e^z-XY)Zy=XZ/(e^z-XY)dZ=Zxdx+Zydy=(ydx+xdy)Z/(e^z-xy)再问:设F(x,y,z)=e^z-xyzə
symsx>>y=log(x+sqrt(1+x^2));>>simple(diff(y)ans=1/(1+x^2)^(1/2)>>y=log(2*x+sqrt(1+x^2));>>simple(dif
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
是∫(x^2-2yz)dx+∫(y^2-2xz)dy+∫(z^2-2xy)dz=x³/3+y³/3+z³/3-2xyz+C=(x³+y³+z³
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
f(x)=ln(1+x)df(x)=dx/(1+x)当x很小时,f(x)-f(0)≈f'(0)*x=x/(1+0)=x总结成公式:ln(1+x))≈x取x=0.01ln(1.01)≈ln(1+0)+0
zx=1/y,代入y=1得zx=1zy=-(x/y^2)代入x=2,y=1得zy=-2所以dz=dx-2dy
dz=(y+y/(X^2))dx+(x-1/x)dy,
dz/dx=1/y,在(2,1)的值是1dz/dy=-x/y^2,在(2,1)的值是-2所以dz|(2,1)=dx-2dy
zx=1/(1+(x/y)²)*1/y=y/(x²+y²)zy=1/(1+(x/y)²)*(-x/y²)=-x/(x²+y²)所以
dz=[yIn(xy)+y]dx+[xIn(xy)+x]dy分开求导
z=arctanx/y+ln√(x^2+y^2)编微分的符号打不出来,只有用d代替了dz/dx=1/(1+(x/y)^2)*1/y+1/√(x^2+y^2)*1/2√(x^2+y^2)*2x=y/(x
y=[ln(1-x)^2]^2y'=2[ln(1-x)^2]*[ln(1-x)^2]'=2[ln(1-x)^2]*[2ln(1-x)]'=2[ln(1-x)^2]*2*1/(1-x)=4*[ln(1-
对x求偏导:2yz+2xyZ'x=2x+2zZ'x,得Z'x=(x-yz)/(xy-z)对y求偏导:2xz+2xyZ'y=2y+2zZ'y,得Z'y=(y-xz)/(xy-z)所以dz=Z'xdx+Z
原式化为(x+y-1)dx+(x+y-1)dy=0设u函数(u为x,y的函数):du/dx=x+y-1.(1)du/dy=x+y-1.(2)由(1)得.对x积分u=1/2x^2+xy-x+f(y)..