求偏导数题目

Question

求偏导数题目如图，大神写下过程

Answer 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]

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]

y=arctan[(x-y)⁸]是一元隐函数，求偏导数？

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Answer 2

等号右边是y？还是什么追问

是y

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