Find the Derivative of the Given Function $c ( x ) = 3 x \sqrt { x ^ { 9 } + 7 }$

Multiple Choice

Find the derivative of the given function. Simplify and express the answer using positive exponents only. $c ( x ) = 3 x \sqrt { x ^ { 9 } + 7 }$

A) $\frac { 3 \left( 11 x ^ { 9 } - 14 \right) } { 2 \left( x ^ { 9 } + 7 \right) ^ { 1 / 2 } }$
B) $\frac { 3 \left( 9 x ^ { 9 } - 14 \right) } { 2 \left( x ^ { 9 } + 7 \right) ^ { 1 / 2 } }$
C) $\frac { 3 \left( 9 x ^ { 9 } - 14 \right) } { \left( x ^ { 9 } + 7 \right) ^ { 1 / 2 } }$
D) $\frac { 3 \left( 11 x ^ { 9 } + 14 \right) } { 2 \left( x ^ { 9 } + 7 \right) ^ { 1 / 2 } }$
E) $\frac { 3 \left( 9 x ^ { 9 } + 14 \right) } { \left( x ^ { 9 } + 7 \right) ^ { 1 / 2 } }$