Find the Rate of Change of the Distance Between the Origin

Multiple Choice

Find the rate of change of the distance between the origin and a moving point on the graph of $y = x ^ { 2 } + 7$ if $\frac { d x } { d t } = 6$ centimeters per second.

A) $\frac { d D } { d t } = \frac { 12 x ^ { 3 } + 90 x } { \sqrt { x ^ { 4 } + 15 x ^ { 2 } + 49 } }$
B) $\frac { d D } { d t } = \frac { 6 x ^ { 3 } - 20 x } { x ^ { 3 } + 15 x ^ { 2 } + 49 }$
C) $\frac { d D } { d t } = \frac { 12 x ^ { 3 } - 90 x } { \sqrt { x ^ { 3 } + 15 x ^ { 2 } + 49 } }$
D) $\frac { d D } { d t } = \frac { 6 x ^ { 3 } + 90 x } { \sqrt { x ^ { 4 } + 14 x ^ { 2 } + 49 } }$
E) $\frac { d D } { d t } = \frac { 12 x ^ { 3 } + 20 x } { x ^ { 4 } + 12 x ^ { 2 } + 49 }$