x=sin(y/x)+e^2 求dy/dx
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x=sin(y/x)+e^2求dy/dxx=sin(y/x)+e^2求dy/dxx=sin(y/x)+e^2求dy/dxx=sin(y/x)+e^2求dy/dxd(x)=d(sin(y/x)+e^2)
x=sin(y/x)+e^2 求dy/dx
x=sin(y/x)+e^2 求dy/dx
x=sin(y/x)+e^2 求dy/dx
x=sin(y/x)+e^2 求dy/dx
d(x)=d(sin(y/x)+e^2)
dx=dsin(y/x)+de^2
dx=cos(y/x)d(y/x)
dx=cos(y/x)(xdy-ydx)/x^2
x^2dx=xcos(y/x)dy-ycos(y/x)dx
x^2dx+ycos(y/x)dx=xcos(y/x)dy
dy/dx=(x^2+ycos(y/x))/xcos(y/x)
sin(y/x)=x-e^2
y/x=arcsin(x-e^2)
dy/dx=(x^2+ycos(arcsin(x-e^2)))/xcos(arcsin(x-e^2))
x=sin(y/x)+e^2 直接对x求导得
1=cos(y/x)·[(y'·x-y)/x²] =cos(y/x)·[y'/x - (y/x)/x]
其中y/x=arcsin(x-e²)+2kπ,代入上式即可
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