高等数学简答题设z=z(x,y)由方程x次方＋2y次方+3z次方－yz=0.求求＆z比&y

Question

高等数学简答题
设z=z(x,y)由方程x次方＋2y次方+3z次方－yz=0.求求＆z比&y

Answer 1

∵x²+2y²+3z²-yz=0
==>4y+6z(＆z/&y)-z-y(＆z/&y)=0 (等式两端对y求导数)
==>6z(＆z/&y)-y(＆z/&y)=z-4y
==>(6z-y)(＆z/&y)=z-4y
==>＆z/&y=(z-4y)/(6z-y)
∴z关于y的偏导数：＆z比&y=(z-4y)/(6z-y).