Find the derivative of the function. $f ( x ) = - 8 x ^ { 3 } - 2 x ^ { 2 } - 1$
A) $f ^ { \prime } ( x ) = - 24 x ^ { 2 } - 4 x$
B) $f ^ { \prime } ( x ) = - 16 x ^ { 2 } - 2 x$
C) $f ^ { \prime } ( x ) = - 16 x - 2 x ^ { 2 }$
D) $f ^ { \prime } ( x ) = - 24 x ^ { 2 } - 4 x - 1$
E)none of the above

Question

Quizplus · Accepted Answer

To find the derivative of $f(x) = -8x^3 - 2x^2 - 1$, apply the power rule for each term: $\frac{d}{dx}(-8x^3) = -24x^2$, $\frac{d}{dx}(-2x^2) = -4x$, and $\frac{d}{dx}(-1) = 0$. Thus, $f'(x) = -24x^2 - 4x$.

Find the Derivative of the Function f(x)=−8x3−2x2−1f ( x ) = - 8 x ^ { 3 } - 2 x ^ { 2 } - 1f(x)=−8x3−2x2−1

Find the Derivative of the Function $f ( x ) = - 8 x ^ { 3 } - 2 x ^ { 2 } - 1$