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Suppose F(x, Y)is a Function of X and Y and Define

question 53

Essay

Suppose f(x, y)is a function of x and y and define g(u,v)=f(eu+cosv,eu+sin(v))g ( u , v ) = f \left( e ^ { u } + \cos v , e ^ { u } + \sin ( v ) \right) Find gu(0,0)g _ { u } ( 0,0 ) given that f(0,0)=5,f(2,1)=1,fx(0,0)=2,fx(1,2)=1,fx(2,1)=3f ( 0,0 ) = 5 , f ( 2,1 ) = - 1 , f _ { x } ( 0,0 ) = 2 , f _ { x } ( 1,2 ) = 1 , f _ { x } ( 2,1 ) = - 3 \text {, } and g(0,0)=1,g(2,1)=1,fy(0,0)=2,fy(2,1)=3,f(1,2)=7g ( 0,0 ) = - 1 , g ( 2,1 ) = - 1 , f _ { y } ( 0,0 ) = 2 , f _ { y } ( 2,1 ) = - 3 , f ( 1,2 ) = 7


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