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

Question

Quizplus · Accepted Answer

The derivative of $f(x) = \frac{8}{x}$ using the power rule is found by rewriting the function as $8x^{-1}$ and then applying the derivative rule for power functions, $d/dx[x^n] = nx^{n-1}$, resulting in $-8x^{-2}$ or $-\frac{8}{x^2}$.

Find the Derivative of the Function Using the Definition of Derivative