Calculate the derivative of the function. Then find the value of the derivative as specified.
-$$f ( x ) = \frac { 8 } { x + 2 } ; f ^ { \prime } ( 0 )$$
A) $f ^ { \prime } ( x ) = - \frac { 8 } { ( x + 2 ) ^ { 2 } } ; f ^ { \prime } ( 0 ) = - 2$
B) $\mathrm { f } ^ { \prime } ( \mathrm { x } ) = 8 ; \mathrm { f } ^ { \prime } ( 0 ) = 8$
C) $f ^ { \prime } ( x ) = \frac { 8 } { ( x + 2 ) ^ { 2 } } ; f ^ { \prime } ( 0 ) = 2$
D) $f ^ { \prime } ( x ) = - 8 ( x + 2 ) ^ { 2 } ; f ^ { \prime } ( 0 ) = - 32$

Question

Quizplus · Accepted Answer

The derivative of $f(x) = \frac{8}{x + 2}$ using the quotient rule or recognizing it as a constant times $x^{-1}$ is $f'(x) = -\frac{8}{(x + 2)^2}$. Substituting $x = 0$ gives $f'(0) = -\frac{8}{(0 + 2)^2} = -\frac{8}{4} = -2$.

Calculate the Derivative of the Function f(x)=8x+2;f′(0)f ( x ) = \frac { 8 } { x + 2 } ; f ^ { \prime } ( 0 )f(x)=x+28​;f′(0)

Calculate the Derivative of the Function $f ( x ) = \frac { 8 } { x + 2 } ; f ^ { \prime } ( 0 )$