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13问答网 > 设w=f(x+y+z,xyz),其中函数f有二阶连续偏导数，求Ȣw⼀Ȣx和Ȣ^2w⼀ȢxȢz

设w=f(x+y+z,xyz),其中函数f有二阶连续偏导数，求Ȣw⼀Ȣx和Ȣ^2w⼀ȢxȢz

2025-03-15 17:54:28

推荐回答（2个）

回答1：

令u=x+y+z,v=xyz
∂f/∂u=f'1,∂f/∂v=f'2
∂w/∂x=∂f/∂u*∂u/∂x+∂f/∂v*∂v/∂x (∵∂u/∂x=1,∂v/∂x=yz)
=f'1+yzf'2
∂2w/∂x∂z=∂(∂w/∂x)/∂z=∂f'1/∂z+yf'2+yz∂f'2/∂z
yf'2+yz∂f'2/∂z是yzf'2对z的导数，由导数的乘法法则得到。
是否可以解决您的问题？

回答2：

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