求全导数u=arcsin(x/y),y=根号(x^2+1),求du/dy
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u=arcsin(x/y)

y=√(x^2+1) dy/dx=2x*(1/2)/√(x^2+1)=x/√(x^2+1)

dx/dy=√(x^2+1)/x

d(x/y)/dy=(dx/dy)/y-x/y^2

=[√(x^2+1)/x ] /√(x^2+1) -x/y^2

=1/x-x/y^2

du/d(x/y)=1/√1-(x/y)^2=y/√(y^2-x^2)=y

du/dy=du/d(x/y)* d(x/y)/dy

=y*[1/x-x/y^2]=y/x-x/y

y=√(x^2+1) x=√(y^2-1)或 x=-√(y^2-1)

du/dy= y/√(y^2-1) -√(y^2-1)/y 或 du/dy= -y/√(y^2-1) +√(y^2-1)/y

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