Find $f ^ { \prime \prime \prime } ( x )$ if $f ( x ) = \frac { 1 } { \sqrt { 3 x } } - \frac { 1 } { x ^ { 2 } } + \sqrt { 6 }$ .
A) $f ^ { \prime \prime \prime } ( x ) = - \frac { 3 } { 8 x ^ { 3 } \sqrt { 3 x } } + \frac { 1 } { x ^ { 3 } }$
B) $f ^ { \prime \prime \prime } ( x ) = - \frac { 15 } { 16 x ^ { 3 } \sqrt { 3 x } } + \frac { 24 } { x ^ { 5 } }$
C) $f ^ { \prime \prime \prime } ( x ) = - \frac { 15 } { 8 x ^ { 3 } \sqrt { 3 x } } + \frac { 24 } { x ^ { 5 } }$
D) $f ^ { \prime \prime \prime } ( x ) = - \frac { 5 } { 72 x ^ { 3 } \sqrt { 3 x } } + \frac { 24 } { x ^ { 5 } }$

Question

Quizplus · Accepted Answer

The third derivative of $f(x)$ is calculated by differentiating the function three times. The correct expression for $f ^ { \prime \prime \prime } ( x )$ is $- \frac { 15 } { 8 x ^ { 3 } \sqrt { 3 x } } + \frac { 24 } { x ^ { 5 } }$.

Find f′′′(x)f ^ { \prime \prime \prime } ( x )f′′′(x)

Find $f ^ { \prime \prime \prime } ( x )$