Answer
$$\frac{d y}{d \theta}=\sin \left(\log _{7} \theta\right)+\frac{1}{\ln 7} \cos \left(\log _{7} \theta\right)$$
Work Step by Step
Given $$ y =\theta \sin \left(\log _{7} \theta\right)$$
Since $$\log_{a}z=\frac{\ln z}{\ln a}$$ So, we have
\begin{aligned}
y&=\theta \sin \left(\log _{7} \theta\right)\\
&=\theta \sin \left(\frac{\ln \theta}{\ln 7}\right)\\
& \Rightarrow \frac{d y}{d \theta}=\sin \left(\frac{\ln \theta}{\ln 7}\right)+\theta\left[\cos \left(\frac{\ln \theta}{\ln 7}\right)\right]\left(\frac{1}{\theta \ln 7}\right)\\
&\ \ \ \ \ \ \ \ \ \ \ \ \ =\sin \left(\log _{7} \theta\right)+\frac{1}{\ln 7} \cos \left(\log _{7} \theta\right)\\
\end{aligned}
