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数学题!紧急!设z=(x+y)^xy,求dz.谢谢!
题目详情
数学题!紧急!
设z=(x+y)^xy,求dz.谢谢!
设z=(x+y)^xy,求dz.谢谢!
▼优质解答
答案和解析
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
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
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