Determine whether the vector field is conservative. If it is, find a potential function for the vector field.
$\overrightarrow { \mathbf { F } } ( x , y ) = 10 x ^ { 9 } y \hat { \mathbf { i } } + x ^ { 10 } { \hat { j } }$
A) conservative with potential function $f ( x , y , z ) = x ^ { 10 } y$
B) conservative with potential function $f ( x , y , z ) = x y ^ { 10 }$
C) conservative with potential function $f ( x , y , z ) = x ^ { 11 } y$
D) conservative with potential function $f ( x , y , z ) = x y ^ { 11 }$
E) not conservative

Question

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The Answer of Determine whether the vector field is conservative. If it is, find a potential function for the vector field.
$\overrightarrow { \mathbf { F } } ( x , y ) = 10 x ^ { 9 } y \hat { \mathbf { i } } + x ^ { 10 } { \hat { j } }$
A) conservative with potential function $f ( x , y , z ) = x ^ { 10 } y$
B) conservative with potential function $f ( x , y , z ) = x y ^ { 10 }$
C) conservative with potential function $f ( x , y , z ) = x ^ { 11 } y$
D) conservative with potential function $f ( x , y , z ) = x y ^ { 11 }$
E) not conservative

Determine Whether the Vector Field Is Conservative F→(x,y)=10x9yi^+x10j^\overrightarrow { \mathbf { F } } ( x , y ) = 10 x ^ { 9 } y \hat { \mathbf { i } } + x ^ { 10 } { \hat { j } }F(x,y)=10x9yi^+x10j^​

Determine Whether the Vector Field Is Conservative $\overrightarrow { \mathbf { F } } ( x , y ) = 10 x ^ { 9 } y \hat { \mathbf { i } } + x ^ { 10 } { \hat { j } }$