x=y+arctany 求隐函数的导数dy/dx.

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x=y+arctany 求隐函数的导数dy/dx.
x=y+arctany 求隐函数的导数dy/dx.

x=y+arctany 求隐函数的导数dy/dx.
y+arctany-x=0
dy/dx+1/(1+y^2)dy/dx-1=0
dy/dx(1+1/(1+y^2)=1
dy/dx=(1+y^2)/(2+y^2)

x=y+arctany
1=y'+1/(1+y²)*y'
=(2+y²)/(1+y²)*y'
所以
y'=(1+y²)/(2+y²)

等式两边同时对x求导得1=y'+y'/(1+y^2)
所以y'=(1+y^2)/(2+y^2)
则隐函数的导数dy/dx=(1+y^2)/(2+y^2)