Question

xy=e^(x+y)的隐函数导数dy/dx如何求?

xy=e^(x+y)的隐函数导数dy/dx如何求?

Answer 1

边对x求导有
y+xy' = e^(x+y) * (1+y')

解得 dy/dx =y'=(e^(x+y)-y)/ ( x-e^(x+y))

Answer 2

就是把y看做x的函数，y(x),对y(x)关于x求导，y(x)+xy'(x)=[1+y'(x)]*e(x+y),再化简为y'(x)=dy/dx={[1+y'(x)]*e(x+y)-y'(x)}/x