Question

大佬们这两题怎么求偏导数

在线等，希望能有大佬可以详细讲一下，谢谢！！！

Answer 1

(1) f'x = 1+ [(y-1)/√(1-x/y)][(1/2)√(y/x)](1/y) = 1+ (1/2)(y-1)/√[x(y-x)]
f'y = arcsin√(x/y) + [(y-1)/√(1-x/y)][(1/2)√(y/x)](-x/y^2)
= arcsin√(x/y) - (1/2)(y-1)√x/[y√(y-x)]
在点（1,1）处， 偏导数不存在。
(1) f'x = cosx + 2x(y-1)/(x^2+y^2) , f'x(0, 1) = 1

Answer 2

1) f'x(x,1)
= lim{x->1}[f(x,1) - f(1,1)]/(x-1)
= lim{x->1} (x-1)/(x-1)
= 1
f'y(1, y)
= lim{y->1}[f(1,y) - f(1,1)]/(y-1)
= lim{y->1}[1+(y-1)arcsin√(1/y) -1]/(y-1)
= lim{y->1}[(y-1)arcsin√(1/y)]/(y-1)
= arcsin1
= π/2
2)
f'x(0,1)
= lim{x->0} [f(x,1)-f(0,1)]/x
= lim{x->0} [sinx-0]/x
= 1