求偏导函数f(x,y)=arctany⼀x,求fx(1,1),fy(-1,-1)

2024-11-28 20:53:18
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回答(1):

f'x(x,y)=1/(1+y²/x²) *(y/x)'=1/(1+y²/x²)(-y/x²)=-y/(x²+y²)
f'y(x, y)=1/(1+y²/x²)*(y/x)'=1/(1+y²/x²)(1/x)=x/(x²+y²)
f'x(1,1)=-1/2
f'y(-1, -1)=-1/2