Find the derivative of the function using the definition of derivative.
-$$f ( x ) = \frac { 8 } { x + 2 }$$
A) $f ^ { \prime } ( x ) = - 8 ( x + 2 ) ^ { 2 }$
B) $f ^ { \prime } ( x ) = 8$
C) $ f ^ { \prime } ( x ) = \frac { 8 } { ( x + 2 ) ^ { 2 } }$
D) $f ^ { \prime } ( x ) = - \frac { 8 } { ( x + 2 ) ^ { 2 } }$

Question

Quizplus · Accepted Answer

The derivative of $f(x) = \frac{8}{x+2}$ using the definition involves applying the quotient rule or the power rule after rewriting the function as $8(x + 2)^{-1}$. Differentiating gives $f'(x) = -8(x + 2)^{-2}$, which simplifies to $-\frac{8}{(x + 2)^2}$.

Find the Derivative of the Function Using the Definition of Derivative