Find the Derivative of the Function $$f ( x ) = \left( x ^ { 2 } + 1 \right) \left( \frac { 9 x - 1 } { 7 x + 1 } \right)$$

Multiple Choice

Find the derivative of the function.
$$f ( x ) = \left( x ^ { 2 } + 1 \right) \left( \frac { 9 x - 1 } { 7 x + 1 } \right)$$

A) $\frac { 63 x ^ { 3 } + 135 x ^ { 2 } + 49 x + 9 } { 7 ( 7 x + 1 ) ^ { 2 } }$
B) $\frac { 63 x ^ { 3 } + 135 x ^ { 2 } + 49 x + 9 } { 7 ( 7 x + 1 ) }$
C) $\frac { 126 x ^ { 3 } + 20 x ^ { 2 } - 2 x + 16 } { ( 7 x + 1 ) ^ { 2 } }$
D) $\frac { 126 x ^ { 3 } + 20 x ^ { 2 } - 2 x + 16 } { ( 7 x + 1 ) }$