多元函数微分

来源:学生作业帮助网 编辑:作业帮 时间:2024/03/29 14:35:14

多元函数微分

z=y/f(x^2-y^2)
zf(x^2-y^2)=y
z'y f(x^2-y^2)+z df(x^2-y^2)/dy=1
z'y f(x^2-y^2)+z df/d(x^2-y^2) *(-2y)=1
z'x f(x^2-y^2)+zdf(x^2-y^2)/dx=0
z'x f(x^2-y^2) +zdf/d(x^2-y^2) *(2x)=0
z'y f/(-2y)+1/2y=z'x f/(2x)
1/y=f* (z'x/x +z'y/y)
1/(fy)=z'x/x+z'y/y
z/y^2=z'x/x+z'y/y