15问答网 > 全微分精通者帮忙！设z=z(x,y)由方程e的z次方-xy的2次方+sin(y+z)=0确定，求dz

全微分精通者帮忙！设z=z(x,y)由方程e的z次方-xy的2次方+sin(y+z)=0确定，求dz

2025-05-15 15:41:13

推荐回答（2个）

回答1：

方程e的z次方-xy的2次方+sin(y+z)=0
e^z-xy^2+sin(y+z)=0
设F＝e^z-xy^2+sin(y+z)
F分别对x、y、z求导
Fx^'=-y^2
Fy^'=-2xy+cos(y+z)
Fz^'=e^z+cos(y+z)
Z对x的偏导数为　　-Fx^'/Fz^'＝y^2/[e^z+cos(y+z)]
Z对y的偏导数为　　-Fy^'/Fz^'＝-[-2xy+cos(y+z)]/[e^z+cos(y+z)]＝[2xy-cos(y+z)]/[e^z+cos(y+z)]
dz=-Fx^'/Fz^'dx+-Fy^'/Fz^'dy
=y^2/[e^z+cos(y+z)]dx+[2xy-cos(y+z)]/[e^z+cos(y+z)]dy

回答2：

(y^2+2xy-cos(y+z))/(e^z+cos(y+z))

全微分精通者帮忙！ 设z=z(x,y)由方程e的z次方-xy的2次方+sin(y+z)=0确定，求dz

全微分精通者帮忙！设z=z(x,y)由方程e的z次方-xy的2次方+sin(y+z)=0确定，求dz