Find the Gradient Vector for the Scalar Function $f ( x , y ) = 10 x ^ { 2 } + 8 x y + 3 y ^ { 2 }$

Multiple Choice

Find the gradient vector for the scalar function. (That is, find the conservative vector field for the potential function.) $f ( x , y ) = 10 x ^ { 2 } + 8 x y + 3 y ^ { 2 }$

A) $\nabla f ( x , y ) = ( 6 y + 8 x ) \hat { \mathbf { i } } - ( 20 x + 8 y ) \hat { \mathbf { j } }$
B) $\nabla f ( x , y ) = 6 y \hat { \mathbf { i } } - 20 x \hat { \mathbf { j } }$
C) $\nabla f ( x , y ) = 6 y \hat { \mathbf { i } } + 20 x \hat { \mathbf { j } }$
D) $\nabla f ( x , y ) = ( 20 x + 8 y ) \hat { \mathbf { i } } + ( 6 y + 8 x ) \hat { \mathbf { j } }$
E) $\nabla f ( x , y ) = 20 x \hat { \mathbf { i } } + 6 y \hat { \mathbf { j } }$