Estimate $g ^ { \prime } ( 6 )$ of the function $g ( t ) = \frac { 1 } { t ^ { 5 } }$ .
A) $- \frac { 5 } { 46,656 }$
B) $- \frac { 1 } { 46,676 }$
C) $- \frac { 1 } { 46,646 }$
D) $- \frac { 1 } { 46,651 }$
E) $\frac { 1 } { 46,656 }$

Question

Estimate $g ^ { \prime } ( 6 )$ of the function $g ( t ) = \frac { 1 } { t ^ { 5 } }$ .  
A) $- \frac { 5 } { 46,656 }$
B) $- \frac { 1 } { 46,676 }$
C) $- \frac { 1 } { 46,646 }$
D) $- \frac { 1 } { 46,651 }$
E) $\frac { 1 } { 46,656 }$

Quizplus · Accepted Answer

To estimate $g ^ { \prime } ( 6 )$, we first find the derivative of $g(t) = \frac { 1 } { t ^ { 5 } }$. The derivative, using the power rule, is $g ^ { \prime } ( t ) = -5t^{-6}$. Plugging in $t = 6$, we get $g ^ { \prime } ( 6 ) = -5(6)^{-6} = - \frac { 5 } { 46,656 }$.

Estimate g′(6)g ^ { \prime } ( 6 )g′(6) Of the Function

Estimate $g ^ { \prime } ( 6 )$ Of the Function