Question

Let  

z equals f left parenthesis x comma y right parenthesis commaz=f(x,y) ,

where

x equals u squared plus v squared and y equals StartFraction u Over v EndFractionx=u2+v2  and  y=uv.

Find

StartFraction partial derivative z Over partial derivative u EndFraction and StartFraction partial derivative z Over partial derivative v EndFraction∂z∂u  and  ∂z∂v

at  

left parenthesis u comma v right parenthesis equals left parenthesis negative 6 comma negative 6 right parenthesis(u,v)=(−6,−6)

​,

given that​ :

f Subscript x Baseline left parenthesis negative 6 comma negative 6 right parenthesis equals 3 comma f Subscript y Baseline left parenthesis negative 6 comma negative 6 right parenthesis equals 12 comma f Subscript x Baseline left parenthesis 72 comma 1 right parenthesis equals 12 comma and f Subscript y Baseline left parenthesis 72 comma 1 right parenthesis equals 24.fx(−6 , −6)=3 ,  fy(−6 , −6)=12 ,  fx(72 , 1)=12 ,  and  fy(72 , 1)=24.

StartFraction partial derivative z Over partial derivative u EndFraction equals∂z∂u=nothing

​, and  

StartFraction partial derivative z Over partial derivative v EndFraction equals∂z∂v=nothing