$$\text { Find the derivative of } y \text { with respect to } x , t , \text { or } \theta \text {, as appropriate. }$$
-$$y = e ^ { \sin t } \left( \ln t ^ { 3 } + 7 \right)$$
A) $e ^ { \sin t } \left( \ln t ^ { 3 } + 7 + \frac { 3 } { t } \right)$
B) $e ^ { \cos t } ( \cos t ) \left( \ln t ^ { 3 } + 7 \right) + \frac { 3 e ^ { \sin t } } { t }$
C) $\frac { 3 \mathrm { e } ^ { \sin t } \cos t } { t }$
D) $e ^ { \sin t } \left( ( \cos t ) \left( \ln t ^ { 3 } + 7 \right) + \frac { 3 } { t } \right)$

Question

Quizplus · Accepted Answer

To find the derivative of y with respect to t, we use the product rule and the chain rule:

$$y' = e ^ {\sin t}(\cos t)(\ln t^3+7)+e^{\sin t}\left(\frac{3}{t}\right)$$

Simplifying this expression, we get:

$$y' = e ^ { \sin t } \left( ( \cos t ) \left( \ln t ^ { 3 } + 7 \right) + \frac { 3 } { t } \right)$$

Therefore, the correct answer is choice D.

Find the derivative of y with respect to x,t, or θ, as appropriate. \text { Find the derivative of } y \text { with respect to } x , t , \text { or } \theta \text {, as appropriate. } Find the derivative of y with respect to x,t, or θ, as appropriate.

$\text { Find the derivative of } y \text { with respect to } x , t , \text { or } \theta \text {, as appropriate. }$