Compute the Gradient of the Function at the Given Point $$f ( x , y , z ) = 2 x y ^ { 3 } z ^ { 2 } , \quad ( 2,8,4 )$$

Multiple Choice

Compute the gradient of the function at the given point.
- $$f ( x , y , z ) = 2 x y ^ { 3 } z ^ { 2 } , \quad ( 2,8,4 )$$

A) ${\nabla} f = 16,384 \mathbf { i } + 8192 \mathbf { j } + 24,576 \mathbf { k }$
B) ${\nabla} f = \mathbf { i } + 12,288 \mathbf { j } + 4096 \mathbf { k }$
C) ${\nabla} f = \quad \mathbf { i } + 8192 \mathbf { j } + 6144 \mathbf { k }$
D) ${\nabla} f = 16,384 i + 12,288 j + 16,384 \mathbf { k }$