Find the value of the first- order derivative of the function
$y = 3 \sqrt { x } - \frac { 81 } { x } + 13$ when x = 9.
A)1
B)1.5
C)- 0.5
D)0
E)0.5

Question

Find the value of the first- order derivative of the function 
$y = 3 \sqrt { x } - \frac { 81 } { x } + 13$ when x = 9.
A)1
B)1.5
C)- 0.5
D)0
E)0.5

Quizplus · Accepted Answer

We need to find the first order derivative of the given function with respect to x, which is given by:
$y' = \frac { 3 } { 2\sqrt { x } } + \frac { 81 } { x^{ 2 } }$
Substituting x=9:
$y' = \frac { 3 } { 2\sqrt { 9 } } + \frac { 81 } { 9^{ 2 } } = \frac { 3 } { 6 } + \frac { 81 } { 81 } = \frac { 1 } { 2 } + 1 = \frac { 3 } { 2 }$
Therefore, the value of the first order derivative of the function when x=9 is 1.5. Hence, the answer is B.

Find the Value of the First- Order Derivative of the Function