Find the derivative of the function. $f ( x ) = \frac { 1 } { x ^ { 4 } }$
A) $f ^ { \prime } ( x ) = - \frac { 3 } { x ^ { 5 } }$
B) $f ^ { \prime } ( x ) = - \frac { 4 } { x ^ { 3 } }$
C) $f ^ { \prime } ( x ) = - \frac { 4 } { x ^ { 5 } }$
D) $f ^ { \prime } ( x ) = - \frac { 5 } { x ^ { 5 } }$
E)none of the above

Question

Quizplus · Accepted Answer

The derivative of $f(x) = \frac{1}{x^4}$ can be found by using the power rule for differentiation, which states that if $f(x) = x^n$, then $f'(x) = nx^{n-1}$. Rewriting the function as $f(x) = x^{-4}$, applying the power rule gives $f'(x) = -4x^{-4-1} = -4x^{-5} = -\frac{4}{x^5}$.

Find the Derivative of the Function f(x)=1x4f ( x ) = \frac { 1 } { x ^ { 4 } }f(x)=x41​

Find the Derivative of the Function $f ( x ) = \frac { 1 } { x ^ { 4 } }$