ln(1 x² y²)的全微分
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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
第一题,这是个隐函数,两边对x求导得:2y'-1=(1-y')*ln(x-y)+(x-y)*(1-y')/(x-y)=(1-y')*ln(x-y)+(1-y')所以[3+ln(x-y)]y'=ln(x
等式两边同时求导得:2y*y'+y'/y=4*x^3-->y'=4y*x^3/(2y^2+1)y'=dy/dx-->dy=y'*dx=dx*4y*x^3/(2y^2+1)
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
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
y=ln[x+√(1+x²)]∴y'=[x+√(1+x²)]'/[x+√(1+x²)]=[1+x/√(1+x²)]/[x+√(1+x²)]=[x+√(
dz(x=0,y=-1)=-2dy 详解如图
解y=ln²(1-2x)y'=dy/dx=[ln²(1-2x)]'=2ln(1-2x)[ln(1-2x)]'(1-2x)'=2ln(1-2x)[1/(1-2x)(-2)=[-4ln
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-
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=1/2*ln(x^2+y^2+4)Z'x=1/2*1/(x^2+y^2+4)*(2x)=x/(x^2+y^2+4)Z'y=1/2*1/(x^2+y^2+4)*(2y)=y/(x^2+y^2+4)所
dz=1/y/(1+x^2/y^2)*dx-x/y^2/(1+x^2/y^2)*dy
dz=1/(1+(x/1+y^2)^2)*(dx/1+y^2)-1/(1+(x/1+y^2)^2)*x*(2ydy/1+y^2)^2
对等式两边求全微分du=【1/(2x+3y+4z^2)】【2dx+3dy+8zdz】
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
全微分后=2x/(3+x^2+y^2)+2y/(3+x^2+y^2)=2/(3+1+4)+4/(3+1+4)=3/4
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