Find the Velocity for the Given Position Vector $\vec { r } ( t ) = \left\langle 2 t , \left( 1 + t ^ { 2 } \right) ^ { 3 } , t \right\rangle$

Multiple Choice

Find the velocity for the given position vector, $\vec { r } ( t ) = \left\langle 2 t , \left( 1 + t ^ { 2 } \right) ^ { 3 } , t \right\rangle$

A) $\vec { v } ( t ) = \left\langle 2 t , \left( 1 + t ^ { 2 } \right) ^ { 3 } , t \right\rangle$
B) $\vec { v } ( t ) = \left\langle 2,6 t \left( 1 + t ^ { 2 } \right) ^ { 2 } , 1 \right\rangle$
C) $\vec { v } ( t ) = \left\langle 2,3 \left( 1 + t ^ { 2 } \right) ^ { 2 } , 1 \right\rangle$
D) $\vec { v } ( t ) = \left\langle 2,3 t ^ { 2 } \left( 1 + t ^ { 2 } \right) ^ { 2 } , 1 \right\rangle$