Use the shortcut rules to calculate the derivative of the given function. $f ( x ) = - 3 x ^ { 0.75 }$
A) $f ^ { \prime } ( x ) = - 3 x ^ { - 0.25 }$
B) $f ^ { \prime } ( x ) = - 2.25 x$
C) $f ^ { \prime } ( x ) = - 3 x ^ { 0.75 }$
D) $f ^ { \prime } ( x ) = - 2.25 x ^ { 0.75 }$
E) $f ^ { \prime } ( x ) = - 2.25 x ^ { - 0.25 }$

Question

Use the shortcut rules to calculate the derivative of the given function.   $f ( x ) = - 3 x ^ { 0.75 }$  
A) $f ^ { \prime } ( x ) = - 3 x ^ { - 0.25 }$
B) $f ^ { \prime } ( x ) = - 2.25 x$
C) $f ^ { \prime } ( x ) = - 3 x ^ { 0.75 }$
D) $f ^ { \prime } ( x ) = - 2.25 x ^ { 0.75 }$
E) $f ^ { \prime } ( x ) = - 2.25 x ^ { - 0.25 }$

Quizplus · Accepted Answer

To find the derivative of $f(x) = -3x^{0.75}$, use the power rule for differentiation: $f'(x) = n \cdot x^{n-1}$, where $n = 0.75$. Thus, $f'(x) = -3 \cdot 0.75 \cdot x^{0.75-1} = -2.25x^{-0.25}$.

Use the Shortcut Rules to Calculate the Derivative of the Given