Question

求解答多元微分问题

多元微分学的不是特别好，这两道题不知道怎么解答，望大家帮忙

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Answer 1

31、f(x，y)=e^x/(x-y)
fx=[e^x(x-y)-e^x]/(x-y)²
fy=-e^x/(x-y)²
fx-fy=e^x/(x-y)=f，选C

Answer 2

31. f(x, y) = e^x/(x-y)
fx = [e^x(x-y)-e^x]/(x-y)^2 = e^x(x-y+1)/(x-y)^2
fy = -e^x(-1)/(x-y)^2 = e^x/(x-y)^2
fx-fy = e^x(x-y)/(x-y)^2 = e^x/(x-y) = f(x, y). 选 C.

追问

第二道题如何解答呢，感谢

追答

f(x, e^z+y) = 0
f'1 + f'2 e^z ∂z/∂x = 0
∂z/∂x = -f'1/(e^zf'2), 选 D。