求偏导，如图，麻烦写出具体过程，谢谢！

更新时间2022-04-10 18:58:04

z = f( x , y ) = √x * sin(y/x)

∂z/∂y = √x * cos(y/x)/x；∂y/∂z= √x/cos(y/x)；

∂z/∂x = sin(y/x)/(2√x) - √x * cos(y/x) * y/x^2 = [ x * sin(y/x) - 2y * cos(y/x) ]/( 2x√x)；

∂y/∂x = ∂y/∂z * ∂z/∂x

= √x/cos(y/x) * [ x * sin(y/x) - 2y * cos(y/x) ]/( 2x√x)

= [ x * sin(y/x) - 2y * cos(y/x) ]/[ 2x * cos(y/x) ]

∂y/∂x|( 1，0 ) = [ 0 - 0 ]/[ 2 ] = 0 。 

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