# 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