Answer
$$\frac{d y}{d t}=\sin t+t \cos t $$
Work Step by Step
Given $$ y=\frac{t \ln \left(\left(e^{\ln 3}\right)^{\sin t}\right)}{\ln 3} $$
Since $$\log_{a}z=\frac{\ln z}{\ln a}$$ So, we have
\begin{aligned}
y& =\frac{t \ln \left(\left(e^{\ln 3}\right)^{\sin t}\right)}{\ln 3}\\
&=\frac{t \ln \left( e^{\sin t\ln 3} \right)}{\ln 3}\\
&=\frac{t\sin t\ln 3 \ln \left( e^{} \right)}{\ln 3}\\
&=t \sin t \\
&\Rightarrow \frac{d y}{d t}=\sin t+t \cos t
\end{aligned}
