Find the indicated derivative. ? $y = 5 \sqrt { x } + \frac { 9 } { \sqrt { x } }$ , $x = 4$ when $t = 1$ , $\left. \frac { \mathrm { d } x } { \mathrm {~d} t } \right| _ { t = 1 } = 5$ ; $\left. \frac { \mathrm { d } y } { \mathrm {~d} t } \right| _ { t = 1 } = $
Please round the answer to the nearest hundredth.

A) $\left. \frac { \mathrm { d } y } { \mathrm {~d} t } \right| _ { t = 1 } = 3.44$
B) $\left. \frac { \mathrm { d } y } { \mathrm {~d} t } \right| _ { t = 1 } = 34.38$
C) $\left. \frac { \mathrm { d } y } { \mathrm {~d} t } \right| _ { t = 1 } = 11.88$
D) $\left. \frac { \mathrm { d } y } { \mathrm {~d} t } \right| _ { t = 1 } = 0.69$
E) $\left. \frac { \mathrm { d } y } { \mathrm {~d} t } \right| _ { t = 1 } = 6.88$

Question

Find the indicated derivative. ? $y = 5 \sqrt { x } + \frac { 9 } { \sqrt { x } }$ , $x = 4$ when $t = 1$ , $\left. \frac { \mathrm { d } x } { \mathrm {~d} t } \right| _ { t = 1 } = 5$ ; $\left. \frac { \mathrm { d } y } { \mathrm {~d} t } \right| _ { t = 1 } =  $  
Please round the answer to the nearest hundredth.
 
A) $\left. \frac { \mathrm { d } y } { \mathrm {~d} t } \right| _ { t = 1 } = 3.44$
B) $\left. \frac { \mathrm { d } y } { \mathrm {~d} t } \right| _ { t = 1 } = 34.38$
C) $\left. \frac { \mathrm { d } y } { \mathrm {~d} t } \right| _ { t = 1 } = 11.88$
D) $\left. \frac { \mathrm { d } y } { \mathrm {~d} t } \right| _ { t = 1 } = 0.69$
E) $\left. \frac { \mathrm { d } y } { \mathrm {~d} t } \right| _ { t = 1 } = 6.88$

Quizplus · Accepted Answer

The correct answer is A.Explanation:$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 5 } { 2 \sqrt { x } } - \frac { 9 } { 2 x ^ { 3 / 2 } }$$\frac { \mathrm { d } y } { \mathrm {~d} t } = \frac { \mathrm { d } y } { \mathrm {~d} x } \cdot \frac { \mathrm { d } x } { \mathrm {~d} t } = \left ( \frac { 5 } { 2 \sqrt { x } } - \frac { 9 } { 2 x ^ { 3 / 2 } } \right ) \cdot 5$$\left. \frac { \mathrm { d } y } { \mathrm {~d} t } \right| _ { t = 1 } = \left ( \frac { 5 } { 2 \sqrt { 4 } } - \frac { 9 } { 2 ( 4 ) ^ { 3 / 2 } } \right ) \cdot 5 = 3.44$

Find the Indicated Derivative y=5x+9xy = 5 \sqrt { x } + \frac { 9 } { \sqrt { x } }y=5x​+x​9​

Find the Indicated Derivative $y = 5 \sqrt { x } + \frac { 9 } { \sqrt { x } }$