x=y+arctany 求隐函数的导数dy/dx.
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/28 17:28:16
x=y+arctany 求隐函数的导数dy/dx.
![x=y+arctany 求隐函数的导数dy/dx.](/uploads/image/z/2050615-55-5.jpg?t=x%3Dy%2Barctany+%E6%B1%82%E9%9A%90%E5%87%BD%E6%95%B0%E7%9A%84%E5%AF%BC%E6%95%B0dy%2Fdx.)
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)
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)