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
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