$\text { Use the quotient rule to differentiate the following function } f ( s ) = \frac { 2 s } { s ^ { 5 } + 7 } \text { and }$ evaluate $f ^ { t } ( - 2 )$
A)$f ^ { t } ( - 2 ) = \frac { 54 } { 5 }$
B)$f ^ { t } ( - 2 ) = - \frac { 54 } { 3125 }$
C)$f ^ { t } ( - 2 ) = \frac { 54 } { 125 }$
D)$f ^ {t } ( - 2 ) = - \frac { 54 } { 5 }$
E)$f ^ { t } ( - 2 ) = - \frac { 54 } { 125 }$

Question

Quizplus · Accepted Answer

Applying the quotient rule,

$$f'(s) = \frac{(s^5+7)(2)-(2s)(5s^4)}{(s^5+7)^2} = \frac{(s^5+7)(2-10s^5)}{(s^5+7)^2}=\frac{2-10s^5}{(s^5+7)^{2}}$$

Now substituting s = -2, we get

$$f^t(-2) = \frac{2-10(-2)^5}{((-2)^5+7)^{2}} = \frac{2-320}{(-32+7)^{2}}=\frac{-318}{(-25)^2}=\boxed{\frac{54}{125}}$$

Use the quotient rule to differentiate the following function f(s)=2ss5+7 and \text { Use the quotient rule to differentiate the following function } f ( s ) = \frac { 2 s } { s ^ { 5 } + 7 } \text { and } Use the quotient rule to differentiate the following function f(s)=s5+72s​ and

$\text { Use the quotient rule to differentiate the following function } f ( s ) = \frac { 2 s } { s ^ { 5 } + 7 } \text { and }$