解：
怎么写？用手写啊！
(1)
令：F(x,y)=x²+xy+y²-100，则：
dy/dx
=-F'x/F'y
=-(2x+y)/(x+2y)
(2)
F(x,y)=e^(x+y) - 10
dy/dx
=-F'x/F'y
=-e^(x+y)/e^(x+y)
=-1
(3)
F(x,y)=xy²+lny+1=0
dy/dx
=-F'x/F'y
=-y²/[2xy+(1/y)]
=-y³/(2xy²+1)
(4)
dy/dx
=-1/(1+cosy)
(5)
dy/dx
=2x/[1-(1/y)]
=2xy/(y-1)
(6)
dy/dx
=-y/(x+e^y)
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