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解:f=arcsin(x-y)^(-1/2)
af/ax=(-1/2)arcsin(x-y)^(-3/2)[arcsin(x-y)]`
=(-1/2)arcsin(x-y)^(-3/2)[1/√(1-(x-y)²)*(x-y)`
=(-1/2)arcsin(x-y)^(-3/2)/[√(1-(x-y)²]
af/ay=(-1/2)arcsin(x-y)^(-3/2)[arcsin(x-y)]`
=(-1/2)arcsin(x-y)^(-3/2)[1/√(1-(x-y)²)*(x-y)`
=(1/2)arcsin(x-y)^(-3/2)/[√(1-(x-y)²]
af/ax=(-1/2)arcsin(x-y)^(-3/2)[arcsin(x-y)]`
=(-1/2)arcsin(x-y)^(-3/2)[1/√(1-(x-y)²)*(x-y)`
=(-1/2)arcsin(x-y)^(-3/2)/[√(1-(x-y)²]
af/ay=(-1/2)arcsin(x-y)^(-3/2)[arcsin(x-y)]`
=(-1/2)arcsin(x-y)^(-3/2)[1/√(1-(x-y)²)*(x-y)`
=(1/2)arcsin(x-y)^(-3/2)/[√(1-(x-y)²]
追问
题目写错了,不好意思,求(y-1)arcsin(x/y)^(1/2)的偏导数
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