Answer
$$\frac{dy}{dt} =\frac{1}{t}\left(\log _{2} 3\right) 3^{\log _{2}t}$$
Work Step by Step
Given $$ y = 3^{\log _{2} t}$$
Since $$\log_{a}z=\frac{\ln z}{\ln a}$$ So, we have
\begin{aligned}
y& = 3^{\log _{2} t}\\
&=3^{\ln t /\ln 2}\\
& \Rightarrow \frac{dy}{dt}=\left[3^{\ln t/ln2}(\ln 3)\right]\left(\frac{1}{t \ln 2}\right)\\
&\ \ \ \ \ \ \ \ \ \ \ \ =\left[3^{\ln t/ln2} \right]\left(\frac{\ln 3}{t \ln 2}\right)\\
&\ \ \ \ \ \ \ \ \ \ \ \ =\frac{1}{t}\left(\log _{2} 3\right) 3^{\log _{2}t}
\end{aligned}
