Find the derivative of the function.
$r ( x ) = \frac { 3 x } { 6 } - \frac { x ^ { 0.6 } } { 2 } + \frac { 8 } { 6 x ^ { 1.6 } } - 8$
A) $r ^ { \prime } ( x ) = \frac { 3 } { 6 } - \frac { 0.6 } { 2 x ^ { 0.4 } } + \frac { 12.8 } { 6 x ^ { 2.6 } }$
B) $r ^ { \prime } ( x ) = \frac { 3 } { 6 } - \frac { 0.6 x ^ { 0.4 } } { 2 } + \frac { 12.8 x ^ { 2.6 } } { 6 }$
C) $r ^ { \prime } ( x ) = \frac { 3 } { 6 } - \frac { 0.6 } { 2 x ^ { 0.4 } } - \frac { 12.8 } { 6 x ^ { 2.6 } }$
D) $r ^ { \prime } ( x ) = \frac { 3 } { 6 } - \frac { 0.6 } { 2 x ^ { 0.6 } } - \frac { 12.8 } { 6 x ^ { 1.6 } }$
E) $r ^ { \prime } ( x ) = \frac { 3 } { 6 } - \frac { 0.6 x ^ { 1.6 } } { 2 } - \frac { 12.8 } { 6 x ^ { 0.6 } }$

Question

Find the derivative of the function. 
$r ( x ) = \frac { 3 x } { 6 } - \frac { x ^ { 0.6 } } { 2 } + \frac { 8 } { 6 x ^ { 1.6 } } - 8$  
A) $r ^ { \prime } ( x ) = \frac { 3 } { 6 } - \frac { 0.6 } { 2 x ^ { 0.4 } } + \frac { 12.8 } { 6 x ^ { 2.6 } }$
B) $r ^ { \prime } ( x ) = \frac { 3 } { 6 } - \frac { 0.6 x ^ { 0.4 } } { 2 } + \frac { 12.8 x ^ { 2.6 } } { 6 }$
C) $r ^ { \prime } ( x ) = \frac { 3 } { 6 } - \frac { 0.6 } { 2 x ^ { 0.4 } } - \frac { 12.8 } { 6 x ^ { 2.6 } }$
D) $r ^ { \prime } ( x ) = \frac { 3 } { 6 } - \frac { 0.6 } { 2 x ^ { 0.6 } } - \frac { 12.8 } { 6 x ^ { 1.6 } }$
E) $r ^ { \prime } ( x ) = \frac { 3 } { 6 } - \frac { 0.6 x ^ { 1.6 } } { 2 } - \frac { 12.8 } { 6 x ^ { 0.6 } }$

Quizplus · Accepted Answer

The derivative of $r(x)$ is found by applying the power rule to each term. The derivative of $3x/6$ is $3/6$, the derivative of $-x^{0.6}/2$ is $-0.6x^{-0.4}/2$, and the derivative of $8/(6x^{1.6})$ is $-12.8/(6x^{2.6})$, taking into account the negative exponent rule. The constant $-8$ disappears as its derivative is 0.

Find the Derivative of the Function r(x)=3x6−x0.62+86x1.6−8r ( x ) = \frac { 3 x } { 6 } - \frac { x ^ { 0.6 } } { 2 } + \frac { 8 } { 6 x ^ { 1.6 } } - 8r(x)=63x​−2x0.6​+6x1.68​−8

Find the Derivative of the Function $r ( x ) = \frac { 3 x } { 6 } - \frac { x ^ { 0.6 } } { 2 } + \frac { 8 } { 6 x ^ { 1.6 } } - 8$