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

Question

Quizplus · Accepted Answer

To find $\mathbf { r } ^ { \prime \prime } ( t )$, we differentiate $\mathbf { r } ( t ) = \left\langle t , t ^ { 9 } , t ^ { 11 } \right\rangle$ twice. The first derivative of $t$ is $1$, of $t^9$ is $9t^8$, and of $t^{11}$ is $11t^{10}$. Differentiating these results again, the second derivative of $t$ is $0$, of $9t^8$ is $72t^7$, and of $11t^{10}$ is $110t^9$, giving $\left( 0,72 t ^ { 7 } , 110 t ^ { 9 } \right\rangle$.

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

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