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

Essay

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