Given that $f_{x}(x, y)=6 x y+y^{2} e^{xy^{2}}$ and $f _ { y } ( x , y ) = 3 x ^ { 2 } + 2 x y e ^ { x y ^ { 2 } }$ Suppose that f(1, 1)= 4.Find the quadratic Taylor polynomial of f(x, y)at (1, 1).

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The Answer of Given that $f_{x}(x, y)=6 x y+y^{2} e^{xy^{2}}$ and $f _ { y } ( x , y ) = 3 x ^ { 2 } + 2 x y e ^ { x y ^ { 2 } }$ Suppose that f(1, 1)= 4.Find the quadratic Taylor polynomial of f(x, y)at (1, 1).

Given That fx(x,y)=6xy+y2exy2f_{x}(x, y)=6 x y+y^{2} e^{xy^{2}}fx​(x,y)=6xy+y2exy2 And fy(x,y)=3x2+2xyexy2f _ { y } ( x , y ) = 3 x ^ { 2 } + 2 x y e ^ { x y ^ { 2 } }fy​(x,y)=3x2+2xyexy2

Given That $f_{x}(x, y)=6 x y+y^{2} e^{xy^{2}}$ And $f _ { y } ( x , y ) = 3 x ^ { 2 } + 2 x y e ^ { x y ^ { 2 } }$