设 e^(x+y) - xy = 1,求 dy/dx \ x=0 y=0如题
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![设 e^(x+y) - xy = 1,求 dy/dx \ x=0 y=0如题](/uploads/image/z/3893387-59-7.jpg?t=%E8%AE%BE+e%5E%28x%2By%29+-+xy+%3D+1%2C%E6%B1%82+dy%2Fdx+%5C+x%3D0+y%3D0%E5%A6%82%E9%A2%98)
设 e^(x+y) - xy = 1,求 dy/dx \ x=0 y=0如题
设 e^(x+y) - xy = 1,求 dy/dx \ x=0 y=0
如题
设 e^(x+y) - xy = 1,求 dy/dx \ x=0 y=0如题
e^(x+y) - xy = 1
两边同时求导,e^(x+y) *(1+dy/dx)-y-xdy/dz=0 (1)
验证 x=0,y=0在原曲线上.令x=0,y=0 代入到(1)
e^0 * (1+dy/dz)-0-0*dy/dz=0
dy/dz|(x=0,y=0)=-1
e^(x+y) - xy = 1 两边对x求导:
e^x*(e^y)*(dy/dx)+e^x*(e^y)-y-x*(dy/dx)=0
将x=0 y=0代入
dy/dx+1=0
dy/dx=-1