设z=f(2x+3y, x/y),f具有二阶连续偏导数,求z...2
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发布时间:2023-11-07 00:05
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时间:2024-07-29 06:45
设 u=x+y,v=x-y,则z=f(u,v),
∴
?z
?x
=
?f
?u
?
?u
?x
+
?f
?v
?
?v
?x
=f′1+f′2,
?z
?y
=
?f
?u
?
?u
?y
+
?f
?v
?
?v
?y
=f′1?f′2,
∴
?2z
?x?y
=
?
?y
(
?z
?x
)=f″11?f″22