Compute the Gradient of the Function at the Given Point $$f ( x , y , z ) = \ln \left( x ^ { 2 } + 5 y ^ { 2 } - 7 z ^ { 2 } \right) , \quad ( 5,5,5 )$$

Multiple Choice

Compute the gradient of the function at the given point.
- $$f ( x , y , z ) = \ln \left( x ^ { 2 } + 5 y ^ { 2 } - 7 z ^ { 2 } \right) , \quad ( 5,5,5 )$$

A) ${\nabla} f = - i - 2 j + \frac { 10 } { 7 } \mathbf { k }$
B) ${\nabla} f = - \frac { 2 } { 5 } \mathbf { i } - 2 \mathbf { j } + \frac { 14 } { 5 } \mathbf { k }$
C) ${\nabla} f = - \frac { 2 } { 5 } \mathbf { i } - 2 \mathbf { j } + \frac { 10 } { 7 } \mathbf { k }$
D) ${\nabla} f = - \mathrm { i } - 2 \mathrm { j } + \frac { 14 } { 5 } \mathbf { k }$