Answer
$$ p^{\prime}=-3 \sin q+\frac{q \cos q-\sin q}{q^{2}}$$
Work Step by Step
Given $$ p=\frac{3 q+\tan q}{q \sec q}$$
So, we have
\begin{aligned} p&=\frac{3 q+\tan q}{q \sec q}\\
&=\frac{3 q}{q \sec q}+\frac{\tan q}{q \sec q}\\
&=\frac{3}{\sec q}+\frac{\frac{\sin q}{\cos q}}{\frac{ q}{\cos q}}\\
&=3 \cos q+\frac{\sin q }{ q}\\
\text{so, we get}\\
p^{\prime}&=-3 \sin q+\frac{q \cos q-\sin q}{q^{2}}\end{aligned}