求下列函数的全微分 u=ln(x² y² z²)
来源:学生作业帮助网 编辑:作业帮 时间:2024/10/02 14:37:06
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
(1)y=3x^2-ln1/x=3x^2+lnxdy=6xdx+(1/x)dx=(6x+1/x)dx(2)y=e^(-x)cosxdy=-e^(-x)cosxdx-e^(-x)sinxdx=-e^(-
令u=2x^2-y^2,v=xy然后链导法则!再问:请您把详细过程给我好吗?再答:偏导数符号打不上去啊du=(4xfu+yfv)dx+(-2yfu+xfv)dy其中fu、fv是偏导数符号
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
ez/ex=1/(x+y^2)*1=1/(x+y^2)ez/ey=1/(x+y^2)*(2y)=2y/(x+y^2)dz=ez/exdx+ez/eydy=1/(x+y^2)dx+2y/(x+y^2)d
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
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
先求出z对x和y的偏导数分别是1/y,-x/y^2所以dz=(1/y)*dx-(x/y^2)*dy
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
点击放大,荧屏放大再放大: