由xy=arctan(y/x) 求dy=?我的计算方法如下:先对两边分别求导(求导过程略),得到[1-(1/x^2+y^2)]y+[x+(x/x^2+y^2)]dy/dx=0然后得到[(x^y+y^3-y)/(x^2+y^2)]+[(x^3+xy^2+x)/(x^2+y^2)]dy/dx=0最后我求出来的dy=[(y-x^y-y^3)/(x+xy^2+x
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![由xy=arctan(y/x) 求dy=?我的计算方法如下:先对两边分别求导(求导过程略),得到[1-(1/x^2+y^2)]y+[x+(x/x^2+y^2)]dy/dx=0然后得到[(x^y+y^3-y)/(x^2+y^2)]+[(x^3+xy^2+x)/(x^2+y^2)]dy/dx=0最后我求出来的dy=[(y-x^y-y^3)/(x+xy^2+x](/uploads/image/z/8562807-63-7.jpg?t=%E7%94%B1xy%3Darctan%28y%2Fx%29+%E6%B1%82dy%3D%3F%E6%88%91%E7%9A%84%E8%AE%A1%E7%AE%97%E6%96%B9%E6%B3%95%E5%A6%82%E4%B8%8B%3A%E5%85%88%E5%AF%B9%E4%B8%A4%E8%BE%B9%E5%88%86%E5%88%AB%E6%B1%82%E5%AF%BC%28%E6%B1%82%E5%AF%BC%E8%BF%87%E7%A8%8B%E7%95%A5%29%2C%E5%BE%97%E5%88%B0%5B1-%281%2Fx%5E2%2By%5E2%29%5Dy%2B%5Bx%2B%28x%2Fx%5E2%2By%5E2%29%5Ddy%2Fdx%3D0%E7%84%B6%E5%90%8E%E5%BE%97%E5%88%B0%5B%28x%5Ey%2By%5E3-y%29%2F%28x%5E2%2By%5E2%29%5D%2B%5B%28x%5E3%2Bxy%5E2%2Bx%29%2F%28x%5E2%2By%5E2%29%5Ddy%2Fdx%3D0%E6%9C%80%E5%90%8E%E6%88%91%E6%B1%82%E5%87%BA%E6%9D%A5%E7%9A%84dy%3D%5B%28y-x%5Ey-y%5E3%29%2F%28x%2Bxy%5E2%2Bx)
由xy=arctan(y/x) 求dy=?我的计算方法如下:先对两边分别求导(求导过程略),得到[1-(1/x^2+y^2)]y+[x+(x/x^2+y^2)]dy/dx=0然后得到[(x^y+y^3-y)/(x^2+y^2)]+[(x^3+xy^2+x)/(x^2+y^2)]dy/dx=0最后我求出来的dy=[(y-x^y-y^3)/(x+xy^2+x
由xy=arctan(y/x) 求dy=?
我的计算方法如下:
先对两边分别求导(求导过程略),
得到[1-(1/x^2+y^2)]y+[x+(x/x^2+y^2)]dy/dx=0
然后得到[(x^y+y^3-y)/(x^2+y^2)]+[(x^3+xy^2+x)/(x^2+y^2)]dy/dx=0
最后我求出来的dy=[(y-x^y-y^3)/(x+xy^2+x^3)]dx
但老师给的答案是dy=[(y+x^y+y^3)/(x-xy^2-x^3)]dx
于是,我想问我这样算有没有什么问题?还是我算错了?
由xy=arctan(y/x) 求dy=?我的计算方法如下:先对两边分别求导(求导过程略),得到[1-(1/x^2+y^2)]y+[x+(x/x^2+y^2)]dy/dx=0然后得到[(x^y+y^3-y)/(x^2+y^2)]+[(x^3+xy^2+x)/(x^2+y^2)]dy/dx=0最后我求出来的dy=[(y-x^y-y^3)/(x+xy^2+x
xy=arctan(y/x),
两边求微分得
ydx+xdy=1/[1+(y/x)^2]*(xdy-ydx)/x^2
=(xdy-ydx)/(x^2+y^2),
∴xdy[1-1/(x^2+y^2)]=-ydx[1+1/(x^2+y^2)],
∴dy=-y(x^2+y^2+1)dx/[x(x^2+y^2-1)]
=[(y+x^y+y^3)/(x-xy^2-x^3)]dx.
您算错了.