Compute the derivative function $f ^ { \prime } ( x )$ algebraically.
$f ( x ) = 8 - 5 x ^ { 3 }$
A) $f ^ { \prime } ( x ) = 15 x ^ { 2 }$
B) $f ^ { \prime } ( x ) = - 15 x$
C) $f ^ { \prime } ( x ) = - 15 x ^ { 2 }$
D) $f ^ { \prime } ( x ) = 8 - 15 x ^ { 2 }$
E) $f ^ { \prime } ( x ) = 10 x ^ { 2 }$

Question

Compute the derivative function $f ^ { \prime } ( x )$ algebraically.  
  $f ( x ) = 8 - 5 x ^ { 3 }$  
A)  $f ^ { \prime } ( x ) = 15 x ^ { 2 }$
B)   $f ^ { \prime } ( x ) = - 15 x$
C)   $f ^ { \prime } ( x ) = - 15 x ^ { 2 }$
D)   $f ^ { \prime } ( x ) = 8 - 15 x ^ { 2 }$
E)   $f ^ { \prime } ( x ) = 10 x ^ { 2 }$

Quizplus · Accepted Answer

The derivative of $f(x) = 8 - 5x^3$ is found by applying the power rule, which gives $f'(x) = 0 - 15x^2$, simplifying to $-15x^2$.

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Compute the Derivative Function $f ^ { \prime } ( x )$