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

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