Question

在下列各题中，求偏导数

Answer 1

计算具体过程如下图所示:

Answer 2

1. u=arctan[(x-y)⁸]

   ∂u/∂x=1/[1+(x-y)¹⁶]·8(x-y)⁷=8(x-y)⁷/[1+(x-y)¹⁶]

   ∂u/∂y=1/[1+(x-y)¹⁶]·-8(x-y)⁷=-8(x-y)⁷/[1+(x-y)¹⁶]

2. u=arctan⁸(x-y)

   ∂u/∂x=8arctan⁷(x-y)·1/[1+(x-y)²]=8arctan⁷(x-y)/[1+(x-y)²]

   ∂u/∂y=8arctan⁷(x-y)·-1/[1+(x-y)²]=-8arctan⁷(x-y)/[1+(x-y)²]

3. y=arctan[(x-y)⁸]是一元隐函数，求偏导数？
   

追问

是我发的题么，为啥还有8次方呢，这个呀