Question

数学题!紧急!设z=(x+y)^xy,求dz.谢谢!？

Answer 1

lnz=xyln(x+y)
两边对x求导得
z'x/z=yln(x+y)+xy/(x+y)
z'x=z[yln(x+y)+xy/(x+y)]
两边对y求导得
z'y/z=xln(x+y)+xy/(x+y)
z'x=z[xln(x+y)+xy/(x+y)]
dz=z'xdx+z'ydy
=z[yln(x+y)+xy/(x+y)]dx+z[xln(x+y)+xy/(x+y)]dy,2,lnz=xyln(x+y)
z'x/z=yln(x+y)+xy'ln(x+y) +xy/(x+y)
z'y/z=xln(x+y)+x'yln(x+y)+xy/(x+y)
dz=(x+y)^(xy)*[(y+xdy/dx)ln(x+y) +xy/(x+y)]dx +(x+y)^(xy)*[(x+dx/dy)ln(x+y)+xy/(x+y)] dy,1,两边取对数，在求微分
z*{(y*dx+x*dy)*ln(x+y)+(x*dx+y*dy)/(x+y)},1,设安排生产A产品的工人有X人，生产B产品的工人有y人，利润为W元，得：因为X≤36，y≤36，5X+4y≤270，所以，4y≤270-5X，y≤（270-5X）/4，,1,