函数z=f(x,y)由方程2sin(x+2y-3z)=x+2y-3z所确定,求dz
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![函数z=f(x,y)由方程2sin(x+2y-3z)=x+2y-3z所确定,求dz](/uploads/image/z/8329136-32-6.jpg?t=%E5%87%BD%E6%95%B0z%3Df%28x%2Cy%29%E7%94%B1%E6%96%B9%E7%A8%8B2sin%28x%2B2y-3z%29%3Dx%2B2y-3z%E6%89%80%E7%A1%AE%E5%AE%9A%2C%E6%B1%82dz)
函数z=f(x,y)由方程2sin(x+2y-3z)=x+2y-3z所确定,求dz
函数z=f(x,y)由方程2sin(x+2y-3z)=x+2y-3z所确定,求dz
函数z=f(x,y)由方程2sin(x+2y-3z)=x+2y-3z所确定,求dz
先两边微分
2cos(x+2y-3z)(dx+2dy-3dz)=(dx+2dy-3dz)
cos(x+2y-3z)=1/2
x+2y-3z=π/3 + 2kπ(三维空间平行平面集合,其实等於几都无所谓,一会再微也没了)
dx+2dy-3dz=0
dz=(dx+2dy)/3
方程两边对x求偏导: 2cos(x+2y-3z)(1-3Z'x)=1-3Z'x, 解得:Z'x=1/3,
方程两边对y求偏导: 2cos(x+2y-3z)(2-3Z'y)=2-3Z'y, 解得:Z'y=2/3
因此dz=Z'xdx+Z'ydy=dx/3+2dy/3
两边全微分。。。