- 设由方程F(x/z,y/z)=0确定了z=f(x,y)则Ax(Z?
- 设由方程F(x/z,y/z)=0确定了z=f(x,y) 则
A x(Z'x)+y(Z'y)=0
B (Z'x)+(Z'y)=z
(Z'x)+(Z'y)==0
D x(Z'x)+y(Z'y)=1
E x(Z'x)+y(Z'y)=Z
其中Z'y表示对y求导
- 选择E
令x/z=u,y/z=v, F(u,v)=0
F'(u)(z-xz'(x))/z^2+F'(v)(-yz'(x)/z^2=0
F'(u)(z-xz'(x))+F'(v)(-yz'(x)=0
z'(x)=zF'(u)/[xF'(u)+yF'(v)]
同理:z'(y)=zF'(v)/[xF'(u)+yF'(v)]
xz'(x)+yz'(y)=[xzF'(u)+yzF'(v)]/[xF'(u)+yF'(v)]=z
E成立