If
$\mathbf { r } ( t ) = \left\langle t , t ^ { 9 } , t ^ { 11 } \right\rangle$ , find $\mathbf { r } ^ { \prime \prime } ( t )$ .
A) $\left\langle 0,110 t ^ { 9 } , 72 t ^ { 7 } \right\rangle$
B) $\left\langle 0,72 t ^ { 6 } , 110 t ^ { 8 } \right\rangle$
C) $\left\langle0,72 t ^ { 7 } , 110 t ^ { 9 } \right\rangle$
D) $\left\langle0,110 t ^ { 8 } , 72 t ^ { 6 } \right\rangle$
E) $\left\langle 1,9 t ^ { 6 } , 11 t ^ { 8 } \right\rangle$

Question

If 
$\mathbf { r } ( t ) = \left\langle t , t ^ { 9 } , t ^ { 11 } \right\rangle$ , find $\mathbf { r } ^ { \prime \prime } ( t )$ .
A) $\left\langle 0,110 t ^ { 9 } , 72 t ^ { 7 } \right\rangle$
B) $\left\langle 0,72 t ^ { 6 } , 110 t ^ { 8 } \right\rangle$
C) $\left\langle0,72 t ^ { 7 } , 110 t ^ { 9 } \right\rangle$
D) $\left\langle0,110 t ^ { 8 } , 72 t ^ { 6 } \right\rangle$
E) $\left\langle 1,9 t ^ { 6 } , 11 t ^ { 8 } \right\rangle$

Quizplus · Accepted Answer

The second derivative of a vector function is found by differentiating each component of the vector function twice. So,$\mathbf { r } ^ { \prime \prime } ( t ) = \left\langle \frac { d ^ { 2 } } { d t ^ { 2 } } t , \frac { d ^ { 2 } } { d t ^ { 2 } } t ^ { 9 } , \frac { d ^ { 2 } } { d t ^ { 2 } } t ^ { 11 } \right\rangle = \left\langle 0,72 t ^ { 7 } , 110 t ^ { 9 } \right\rangle$

If r(t)=⟨t,t9,t11⟩\mathbf { r } ( t ) = \left\langle t , t ^ { 9 } , t ^ { 11 } \right\rangler(t)=⟨t,t9,t11⟩

If $\mathbf { r } ( t ) = \left\langle t , t ^ { 9 } , t ^ { 11 } \right\rangle$