Answer
$$ \frac{d y}{d t} =\frac{1}{(t\ln t)(\ln 2)}$$
Work Step by Step
Given $$ y = 3 \log _{8}\left(\log _{2} t\right)$$
Since $$\log_{a}z=\frac{\ln z}{\ln a}$$ So, we have
\begin{aligned}
y& = 3 \log _{8}\left(\log _{2} t\right)\\
&=\frac{3 \ln \left(\log _{2} t\right)}{\ln 8}\\
&=\frac{3 \ln \left(\frac{\ln t}{\ln2}\right)}{\ln 8} \\
&\Rightarrow \frac{d y}{d t}=\left(\frac{3}{\ln 8}\right)\left[\frac{1}{(\ln t) /(\ln 2)}\right]\left(\frac{1}{t \ln 2}\right)\\
&\ \ \ \ \ \ \ \ \ \ \ \ =\frac{3}{t(\ln t)(\ln 8)}\\
&\ \ \ \ \ \ \ \ \ \ \ \ =\frac{3}{t(\ln t)(\ln 2^3)}\\
&\ \ \ \ \ \ \ \ \ \ \ \ =\frac{3}{3t(\ln t)(\ln 2)}\\
&\ \ \ \ \ \ \ \ \ \ \ \ =\frac{1}{(t\ln t)(\ln 2)}\\
\end{aligned}
